The Production of Cognitive and Non-cognitive Human Capital in the Global Economy Chong Xiang, Purdue University Stephen Ross Yeaple, Penn State University and NBER September 2017
Abstract A country’s welfare is tied to its ability to foster the accumulation of cognitive and non-cognitive human capital. However, we do not fully understand how countries produce them and even struggle with their measurement. For instance, international test scores neglect non-cognitive human capital. In this paper, we develop a multi-country, open-economy general-equilibrium framework where heterogeneous individuals make optimal occupational choices. Because people in non-cognitive (cognitive) occupations primarily use their non-cognitive (cognitive) human capital, by observing people’s occupational choices we can quantify how well countries produce their cognitive and non-cognitive human capital. Our model predicts parsimonious relationships among publically available data, allowing us to extract the full set of parameter values. They show that countries di¤er substantially in the underlying productivities of cognitive and non-cognitive human capital. We then aggregate over these two dimensions to construct a single measure of human-capital productivity, and to demonstrate its implications for cross-country di¤erences in output per worker. Our results have important policy implications: many high-test-score countries fair poorly according to our productivity metrics, and education policies that increase test score may decrease aggregate output. Our results depend on how much countries trade the services of cognitive and non-cognitive human capital: if barriers to such trade were eliminated, the countries with strong comparative advantages in producing cognitive or non-cognitive human capital would reap very large gains in aggregate output.
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1
Introduction
Human capital is central to both economics and other social sciences. Therefore, understanding how well countries produce their human capital is critical for both academic research and for policy. One way these questions are currently answered is to look at the scores of international assessment tests, like PISA. The U.S. generates low test scores despite having one of the highest levels of per-capita educational spending in the world. These low test scores have alarmed policy makers in the U.S.,1 and motivated major policy changes (e.g. No Child Left Behind of 2001 and Race to the Top of 2009). Like the U.S., many other countries worry that their test scores are too low (e.g. U.K., Canada, Slovakia and Qatar).2 Oddly, many countries whose students excel in international exams worried that their educational systems overemphasize formal examination pro…ciency at the expense of less tangible forms of education with the result that their students spend too much time studying for exams!3 This concern has also in‡uenced policy: the Education Ministry in China declared a ban on homework assignments for young children in August 2013, and South Korea declared a 10 pm curfew on private tutoring. The fear is that the educational systems emphasize testing to such a degree that students do not e¤ectively develop other useful skills, such as leadership, co-operation, and communication. While the importance of these non-cognitive skills has been clearly established in academic research (e.g. Heckman and Rubinstein 2001), their quanti…cation and measurement remain challenging, because many of them do not show up in test scores (e.g. Heckman and Kautz 2012). Hanushek and Woessmann (2011) recognize that “the systematic measurement of such skills has yet to be possible in international comparisons”. In this paper, we present a multi-country, open-economy general equilibrium (GE) framework that we have developed to quantify how countries produce human capital 1
e.g. President Obama said that the nation that "out-educates us today will out-compete us tomorrow." 2 For example, in February 2014, Elizabeth Truss, the U.K. education minister, visited Shanghai, China, whose test score is much higher than the U.K.’s, to “learn a lesson a math”. 3 For example, the Wall Street Journal reports that “A typical East Asian high school student often must follow a 5 a.m. to midnight compressed schedule, …lled with class instruction followed by private institute courses, for up to six days a week, with little or no room for socializing” (February 29, 2012), and that “many students prepare for [the national college] entrance exams from an early age, often studying up to 16 hours a day for years to take these tests” (November 10, 2011).
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along multiple dimensions. The starting point of our framework is the observation that peoples’occupational choices reveal information about their skills at di¤erent types of tasks, and part of these skills have been developed through their education. For example, a manager issues directions and guidance to subordinates, a secretary follows these orders, while an engineer uses the knowledge in math and science to solve problems. We follow previous research (e.g. Autor, Levy and Murname 2003) and classify occupations as non-cognitive and cognitive. Because the people in non-cognitive (cognitive) occupations are primarily drawing on their non-cognitive (cognitive) human capital, by observing people’s occupational choices we can quantify how well countries produce their human capital along these dimensions. To be speci…c, we write down production functions of cognitive and non-cognitive human capital, and use the TFP’s (Total Factor Productivity) of these production functions to quantify countries’productivities in accumulating cognitive and non-cognitive human capital. Our inspiration is the strong and intuitive intellectual appeal of TFP and its ubiquitous uses to measure the qualities of production technologies for countries, industries and …rms. Intuitively speaking, a country with a high cognitive (non-cognitive) productivity produces a large quantity of cognitive (non-cognitive) human capital, holding …xed resources inputs. In addition, researchers have long recognized that incentives matter for educational outcomes,4 which is closely related to human capital production. We accommodate incentives in our model by having heterogeneous workers make optimal occupational choices given their own comparative advantages in non-cognitive and cognitive skills, as in Willis and Rosen (1979). These individuals’comparative advantages, in turn, are determined by their innate abilities at birth and human capital accumulated. When workers decide how much human capital to accumulate, they factor in the returns of human capital on the labor market, recognizing that non-cognitive and cognitive occupations require di¤erent types of human capital. This implies that in our model, individual workers’ human capital accumulation is a¤ected by their occupational choices, which, in turn, 4
In empirical studies using micro data, researchers have long recognized that incentives, in the form of money or even candy, improve the scores of IQ tests (Heckman and Kautz 2012). In a recent large-scale …eld experiment in Mexico, Behrman, Parker, Todd, and Wolpin (2015) show that providing monetary incentives to students has substantial and immediate e¤ects on their test scores.Researchers have also shown that instructor incentives matter for the scores of high-stake tests (e.g. Neal and Schanzenbach 2010). PISA, whose scores we use, is not a high-stake test.
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depend on the non-cognitive and cognitive productivities of the economy. For cognitive productivities we use test scores as the starting point, leveraging on the widely available test-score data and building on the insight of the empirical literature on international test scores (e.g. Hanushek and Woessmann 2011). We then peel back the confounding factors of resources inputs and incentives under the guidance of our GE model, to reveal the countries’ underlying productivities in fostering cognitive human capital. Importantly, this procedure remains the same whether our model is closedeconomy, open-economy with free trade, or open-economy with positive trade costs. Our results show that countries’ cognitive-productivity rankings are substantially di¤erent than their PISA-score rankings. In particular, those with the highest test scores do not necessarily have the highest cognitive productivities (e.g. S. Korea, Hong Kong). Our GE model draws on the insight of the empirical literature that examines noncognitive skills using micro data (e.g. Kuhn and Weinberger 2005, Heckman and Kautz 2012). In our model, the ratio of non-cognitive productivity to cognitive productivity of the country’s educational system, i.e. its comparative advantage for non-cognitive human capital, drives workers’ occupational choices, and so comparative advantage in human capital accumulation is revealed by the ratio of occupation employment shares. Intuitively speaking, the fact that many individuals in country k choose the non-cognitive occupation suggests that country k has a strong comparative advantage for non-cognitive human capital. If, in addition, country k has a high absolute advantage in cognitive human capital accumulation, then this country must also have an absolute advantage in non-cognitive human capital accumulation. Here international trade plays an important role. In the closed-economy setting, the relative return of non-cognitive human capital ultimately depends on country k’s comparative advantage for non-cognitive human capital. Therefore, data on occupation employment shares are su¢ cient to back out this comparative advantage. With international trade, however, the relative return of non-cognitive human capital is determined globally. Intuitively speaking, the fact that country k is a large net importer of the service of non-cognitive human capital suggests that it has a strong comparative advantage for non-cognitive human capital, since the non-cognitive workers in k have chosen their occupation despite import competition. Our model delivers an analytical expression for the comparative advantage of human capital production, where the e¤ects of trade are summarized by its factor content in terms of cognitive and non-cognitive human capital. Of course, high barriers to factor content trade shrink the di¤erence between open4
vs. closed-economy settings. This feature of our model is reminiscent of the classic theoretical studies of Deardor¤ and Staiger (1988) and Krugman (2000). While these studies take aggregate factor supplies as …xed, we model how these supplies respond as individuals make optimal choices for human capital accumulation. Looking at our data, we show that non-cognitive productivities are very similar across open- and closed-economy settings. In particular, countries’non-cognitive-productivity rankings have zero correlation with their PISA score rankings, and many countries with low test scores have high non-cognitive productivities (e.g. the U.S. and U.K.). Therefore, non-cognitive productivities are a novel dimension of the quality of human-capital production that not revealed by test scores. Our model then allows us to condense the multi-dimensional di¤erences in cognitive and non-cognitive productivities into a single metric, which we call overall educational quality. This metric is the weighted power mean of cognitive and non-cognitive productivities, the weights being the employment shares of cognitive and non-cognitive occupations. The power coe¢ cients of this metric depend on the following three parameters: the dispersion of workers’innate abilities, which governs the supply-side elasticity of the economy; the substitution-elasticity across di¤erent types of human capital in aggregate production, which governs the demand-side elasticity of the economy; and the output elasticity in the production of human capital. To identify these key parameters, we draw on the parsimonious relationships predicted by our model among publicly available data, such as test score, output per worker, employment shares of non-cognitive and cognitive occupations, and factor content of trade. The simple and transparent ways we identify our parameters, and our unique focus on cross-country di¤erences in the production of human capital, distinguish our work from the quantitative literature on worker heterogeneity and income dispersion (e.g. Ohsornge and Tre‡er 2007, Hsieh, Hurst, Jones and Klenow 2016, Burnstein, Morales and Vogel 2016). We can now graph the combinations of cognitive and non-cognitive productivities that produce the same overall educational quality, borrowing the idea of the isoquant. This iso-education-quality …gure illustrates the large di¤erences in how countries produce their cognitive and non-cognitive human capital. To draw out the economic signi…cance of such di¤erences, we show that the ratio of output per worker between any pair of countries can be decomposed into a power function of the ratio of overall educational quality, multiplied by a power function of the ratio of output TFP. Implementing this exact decomposition using raw data and our model parameters, we show that the di¤erences 5
in human-capital productivities across countries have large implications for output per worker. For example, Germany’s output per worker is 62.96% of the U.S. level (data), of which 88.34% can be attributed to human-capital productivities (model parameters) and 71.26% to output TFP (model parameters). Our paper has some outward similarity to the literature that accounts for variation across countries in income per capita. This literature has focused on the appropriate way to aggregate labor that varies in the number of years of education (e.g. Mankiw, Romer and Weil 1992, Klenow and Rodriguez-Clare 1997, Caselli 2005). Some of the more recent literature, such as Jones (2014) and Malmberg (2017), have improved on this literature by allowing di¤erent educational levels to be imperfect substitutes. None of these papers addresses the issues that years of education do not distinguish between cognitive versus non-cognitive skills, or that individuals optimally choose both the quantities and types of human capital to accumulate. On the other hand, an applied micro literature examines the formation of individual skills using worker-level data (e.g. Cunha, Heckman and Schennach 2010, Jackson, Johnson and Persico 2015). We examine the di¤erent ways in which high-income (and some middle-income) countries produce di¤erent types of human capital, and the implications of such di¤erences for aggregate output and for education policies. More broadly, the ways countries produce their human capital are related to their educational systems, which often have deep historic roots and so are an important part of these countries’ institutions. We thus also contribute to the institutions literature (e.g. Hall and Jones 1999, Acemoglu, Johnson and Robinson 2001) by quantifying key characters of the educational institution and drawing out their implications for aggregate output. Our model and our results have policy implications. Ever since the 1983 report by the National Commission on Excellence in Education, there have been heated debates in the U.S. about the pros and cons of focusing on test scores. We bring the rigor of economic modeling and quantitative analyses into these discussions. In our model, education policies that focus on test scores tend to increase cognitive human capital, but create dis-incentives against non-cognitive human capital and may decrease its quantity in the aggregate economy. Our model quanti…es these pros and cons and calculates the net e¤ect on aggregate output. e.g. we show that if the U.S. were to have Hong Kong’s cognitive and non-cognitive productivities, the U.S. test score would rise but U.S. aggregate output would fall. Such calculations also provide a benchmark for the 6
cost e¤ectiveness and payo¤s of education policies, and clarify that aggregate output is a better goal for education policies than test score. In doing so, we contribute to a large empirical literature using micro data to evaluate the e¤ects of education policies on individual outcome (e.g. Figlio and Loeb 2011). Finally, we use our model to calculate how much countries’aggregate output would be if there were no frictions to trade. Our calculations show large gains from trade liberalization, especially for the countries with strong comparative advantages in producing cognitive (e.g. S. Korea would gain at least 50.63% of its output) or non-cognitive human capital (e.g. the Netherlands would gain at least 27.24%). These gains from trade are large relative to the literature (e.g. Costinot and Rodriguez-Clare 2014), especially given that trade in our model is for homogeneous services with perfect competition. Intuitively, we obtain large gains from trade liberalizations among our sample of high-income countries because they di¤er substantially in how they produce cognitive and non-cognitive human capital. The remainder of this paper is organized as follows. Section 2 discusses the key facts that motivate our theoretical framework. Section 3 sketches this theoretical framework. Section 4 outlines the identi…cation of our structural parameters. Section 5 draws out the implications of our non-cognitive and cognitive productivities. Section 6 explores the quantitative implications of our model. Section 7 concludes.
2
Non-cognitive and Cognitive Occupations, and Other Motivating Data Patterns
A simple way to assess a country’s pro…ciency in human capital production is to use internationally comparable PISA test scores with educational spending per student, as is shown in Figure 1. This …gure shows that more input (spending) leads to more output (test score), with substantial deviations from the best linear predictor (crude measure of productivity). Missing from this naïve assessment is that the non-cognitive skills that are important in a modern work place are not well assessed by examinations, and that a country’s ability to foster these skills will be hard to compare internationally. Moreover, to the extent that a country has a comparative advantage in producing easily measured skills, this country will look productive along this dimension, in part because workers will optimally choose 7
to acquire these skills more at the expense of less quanti…able skills. We now demonstrate that occupations di¤er in the extent to which performance on test scores matters for workplace productivity. We use leadership to measure noncognitive occupations. If the O*NET characteristic “providing guidance and direction to subordinates . . . ”is important for an occupation, we classify it as non-cognitive, and we classify all the other occupations as cognitive. We focus on leadership because it gives us intuitive and plausible correlation patterns in the micro data used by previous studies and also in our own micro data. To be speci…c, Kuhn and Weinberger (2005) use U.S. data to show that those who have leadership experiences during high school have higher wages later in their lives. In addition, we show below, in Table 1, that the wages of leadership occupations are less correlated with test scores than those of the other occupations, using the framework of Neal and Johnson (1996). The data used in Table 1 is the 1979 NLSY (National Longitudinal Survey of Youth). The dependent variable is the log of individuals’wages in 1991, and the main explanatory variable is their AFQT score (Armed Force Quali…cation Test) in 1980, before they enter the labor force. Column 1 shows that the coe¢ cient estimate of AFQT score is positive and signi…cant, and this result replicates Neal and Johnson (1996).5 Columns 2 and 3 show that AFQT score has a smaller coe¢ cient estimate for the subsample of non-cognitive occupations than for the subsample of cognitive occupations.6 To show this pattern more rigorously, we pool the data in column 4 and introduce the interaction between AFQT score and the non-cognitive-occupation dummy. The coe¢ cient estimate of this interaction term is negative and signi…cant.7 In column 5 we use the O*NET characteristic of enterprising skills as an alternative measure for leadership. The interaction between enterprising skills and AFQT score is negative but not signi…cant. 8 5
We include both men and women in Table 1, while Neal and Johnson (1996) do the estimation separately for men and women. We have experimented with this and obtained very similar results. We also use the same sample cuts as Neal and Johnson (1996) (see the Appendix for the details). 6 Note that the coe¢ cient estimates for AFQT square are not signi…cant. 7 Note that (1) we include the non-cognitive dummy itself, plus the college dummy and its interaction with AFQT score; (2) the non-cognitive dummy itself has a positive and signi…cant coe¢ cient estimate, consistent with Kuhn and Weinberger (2005). 8 We have also experimented with using the following O*NET characteristics to measure non-cognitive occupations: investigative skills, originality, social skills, and artistic talents. The results for originality, investigative skills and social skills are counter-intuitive, and artistic talents account for a very small fraction of the labor force. See the Appendix for more details.
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Having classi…ed occupations as non-cognitive and cognitive using the U.S. O*NET, we next bring in employment data by 3- or 4-digit occupations from the International Labor Organization (ILO). We keep only the countries whose raw data are in ISCO-88 (International Standard Classi…cation of Occupations), because O*NET occupations can be easily mapped into ISCO-88 occupations but the mappings among other occupation codes are very scarce (e.g. we cannot …nd the mapping between Canadian and U.S. occupation codes). This leaves us with a single cross-section of 34 countries, and most of them are in 2000. Examples of non-cognitive occupations include business professionals (ISCO-88 code 2410), managers of small enterprises (1310), building frame and related trades workers (7120), nursing and midwifery professionals (3230), etc. Examples for cognitive occupations include architects, engineers and related professionals (2140), …nance and sales professionals (3410), secretaries (4110), motor vehicle drivers (8320), etc. We then merge in mean PISA scores in reading, math and science from the o¢ cial PISA website, and the ratios of private plus public expenditures on education to GDP in 2004 from the UNESCO Global Education Digest of 2007.9 10 Finally, we add other variables, such as labor-force size and aggregate output, from standard sources, such as NIPA (National Income and Product Account) and PWT (Penn World Tables). Because we do not have physical capital in our model, as we show in section 3, we use labor income, or compensation of employees from NIPA, as our measure for aggregate output.11 In addition, in middle-income countries (e.g. Thailand), subsistence farming 9
When PISA …rst started in 2000, only the reading test was administered, and only a small set of countries participated (e.g. the U.K. and Netherlands did not participate). In order to obtain PISA scores in all three subjects for every country in our sample, we calculate simple averages over time by country by subject, using all years of available data; e.g. Germany’s PISA math score is the simple average of 03, 06, 09 and 2012, U.K.’s reading score the average of 06, 09 and 2012, etc. In the Appendix we show that PISA scores have small over-time variation but large cross-section variation. 10 We use PISA scores because they are widely reported in the media, and have in‡uenced education policies in many countries. In addition, PISA samples students in a nationally representative way, covers many countries, and controls qualities of the …nal data (e.g. the 2000 UK scores and 2006 US reading scores are dropped because of quality issues). Finally, while PISA scores are for high-school students, they are highly correlated with the scores of adult tests (e.g. Hanushek and Zhang 2009, our Data Appendix and Table A3). Compared with PISA, adult tests cover substantially fewer countries (they would cut our sample size by at least 25%) and have substantially lower response rates (e.g. Brown et al. 2007, our Data Appendix). 11 We experimented with stripping capital from GDP by assuming a Cobb-Douglas production function
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and/or the informal sector might be an issue, since it is unclear how to think about the contributions of human capital there. We use the 28 high-income countries as our main sample, and examine the extended sample that also includes middle-income countries in section 8. These high-income countries account for 42.94% of world GDP in 2000. Table 2 provides summary statistics of our main variables of interest, and Table 3 lists the countries and years in our sample. Note that all our data come from public sources. To further motivate our model, we now demonstrate that the countries with relative abundance in non-cognitive human capital are in fact net exporters of its service. We follow the literature (e.g. Nunn 2007) and examine the correlation between the patterns of trade and the interactions between relative factor abundance and factor-use intensities. For each country in our sample, we collect aggregate import and export for the 31 NAICS manufacturing industries in the 2000 U.S. census, and the 9 1-digit service industries in the UN service-trade database. To measure trade patterns, we calculate net export divided by the sum of import and export by industry by country. For each country, we measure its relative abundance in non-cognitive human capital, physical capital and skilled labor as, respectively, the noncognitive employment share, the ratio of physical capital stock to population, and the fraction of college-educated labor force. For each industry, we measure the intensities of non-cognitive human capital, physical capital and skilled labor using U.S. data.12 Finally, we control for industry …xed e¤ects and country …xed e¤ects. Table 4 reports the results. Column (1) includes only the interaction for non-cognitive human capital. We add the interaction for physical capital in column (2), and then the interaction for skilled labor in column (3). The interaction for non-cognitive human capital has positive and signi…cant coe¢ cient estimates in all speci…cations.
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A Model of Human Capital Production with Heterogeneous Workers
In this section we develop our model for the production of human capital and illustrate the intuition of our key parameters. A key feature of our model is that heterogeneous and using the parameter values from the macro literature (e.g. Klenow and Rodriguez-Clare 1997). The aggregate output of this second approach has a correlation of 0.9994 with our main output variable. 12 See our Appendix for more details.
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workers optimally choose both the quantities and types of human capital to accumulate. We also show how the model can make contact with observable country outcomes with an eye toward quanti…cation, in preparation for section 4.
3.1
Model Structure
There are K countries, indexed by k, each endowed with Lk units of heterogeneous labor. Workers are endowed with non-cognitive and cognitive attributes "n and "c , drawn from the following Frechet distribution F ("n ; "c ) = exp
Tc "c + Tn "n
1
;
1
e
(1)
In the context of the correlation patterns that we discussed in section 2, we think about the attributes n and c as two distinct packages of skills, rather than two individual skills. These two packages may have common elements. In equation (1), the parameter captures the degree to which non-cognitive and cognitive packages are correlated. When = 0, they are independent; when > 0, they have positive correlation; and when ! 1, they become perfectly collinear. The parameter captures the dispersion of attributes across workers. As rises, the distribution becomes more compressed, and so there is less worker heterogeneity. Note that for the distribution to have …nite variance, we require > 1. Finally, Tc and Tn , both positive, capture the locations of the attributes distribution; e.g. as Tc rises, the distribution of cognitive abilities shifts to the right, so that the average worker has better innate cognitive abilities. We assume that , , Tc , and Tn do not vary across countries.13 To minimize the number of moving parts, we follow Hsieh et al. (2016) and specify the following human-capital production function. Workers accumulate human capital of type i, i = n (non-cognitive) or c (cognitive), according to the technology hi (e) = hki e , i = c; n.
(2)
In equation (2), e is an individual worker’s spending on human capital accumulation, in units of the …nal good (we specify its production below). The parameter captures decreasing returns in the production of human capital, and guarantees an interior solution 13
The assumption over and is standard in the literature using Roy model models. The assumption that the T s are same is that there are no inherent genetic di¤erences across countries.
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for workers’ optimal human-capital spendin, e. We assume that is common across countries. The parameters hkn and hkc are country k’s productivities in non-cognitive and cognitive human capital, and they capture the strength of country k’s educational institution along these two dimensions, net of resources inputs. We treat hkn and hkc as exogenous, because the educational institution has deep historic roots in many countries. For example, in the U.S., private universities and colleges are a main feature of the educational institution, and their legal rights and status were enshrined by the Supreme Court in 1819 in Dartmouth-College-vs-Woodward.14 In S. Korea, and many other East Asian countries, the national exam has been a cornerstone of the educational institution for over 1,000 years.15 We capture, and quantify, such cross-country di¤erences in educational institutions as hkn and hkc , and so we place no restriction on their values. Both non-cognitive and cognitive tasks are needed to produce the …nal good. When a worker chooses task i, or occupation i, her output is (3)
hi (e)"i ; i = n; c
where hi (e) is the quantity of the worker’s human capital, accumulated according to the technology (2), and "i her attribute, drawn from the distribution in (1).16 The representative …rm hires workers in both cognitive and non-cognitive occupations to maximize output yk =
k
Ac Lkc
1
14
+ An Lkn
1
1
(4)
In 1816, New Hampshire enacted state law to convert Dartmouth College from a private institution to a state institution. The case went to the U.S. Supreme Court, the legal issue being whether Dartmouth’s original charter with the King of England should be upheld after the American Revolution. In 1819, the Supreme Court sided with Dartmouth, and this decision also guaranteed the private status of other early colonial colleges, such as Harvard, William and Mary, Yale, and Princeton (e.g. Webb, Metha, and Jordan 2013). 15 China used archery competitions to help make promotion decisions for certain bureaucrateic positions before 256 B.C.E. and established the imperial examination system as early as 605 A.D. and this remained in use for over 1,000 years. In this system, one’s score in the national exam determines whether or not he is appointed to a government o¢ cial, and if so, his rank. Through trade, migration, and cultural exchanges, China’s imperial examination system spread to neighboring countries; e.g. Korea established a similar system in 958 A.D. (Seth, 2002). 16 Equation (3) assumes that occupation i uses skill i. We have experimented with having occupations use both skills, with occupation i being more intensive in skill i. This alternative speci…cation adds little insight but much complexity so we have gone with the simpler set up.
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In equation (4), k is country k’s total-factor productivity (TFP), and Ac and An common technological parameters. The parameter > 0 is the substitution elasticity between non-cognitive and cognitive skills. Lkn and Lkc are the sums of individual workers’ outputs of non-cognitive and cognitive tasks, which are speci…ed in equation (3). Lkn and Lkc can also be interpreted as country k’s aggregate supplies of non-cognitive and cognitive human capital. While we assume that …nal goods cannot be traded, we allow for the possibility that labor inputs Lkc and Lkn can be traded as factor content embodied in intermediate inputs. The key prices in country k are the price of an e¤ective unit of cognitive labor wck , the price of an e¤ective unit of non-cognitive labor wnk , and the price of the …nal output, P k . Given cost minimization of the perfectly competitive …nal goods producers, the price of the …nal good (4) is given by Pk =
1 k
(Ac )
wck
1
+ (An )
wnk
1
1 1
:
(5)
All markets are perfectly competitive. The timing happens as follows. First, workers choose how much and what type (cognitive or non-cognitive) of education to obtain. Second, …nal goods producers choose how many workers of each type to employ and how much of each type of intermediate (cognitive intensitive or non-cognitive intensive) to import. Finally, all markets clear.
3.2
Equilibrium Conditions
We …rst analyze how workers allocate their time to study given their optimal occupational choice. We then consider the aggregate supply of e¤ective labor of cognitive and non-cognitive labor. Having characterized the supply of labor of each type, we then consider the supply side taking into account the supplies of each type of labor supplied via international trade. Recall that the human capital investment is in terms of …nal output so that the proper maximization problem facing an individual that will choose occupation i is max wi hki e e
i
P ke
and so the optimal choice of human capital investment, after substituting for the price
13
index and accounting for the normalization, is then wik k h Pk i
e( i ) =
1 1
i
(6)
:
Equation (6) says that, intuitively, individuals in country k accumulate large quantities of human capital if real wages are high. It also shows that the …nal-good price index, P k , has the same e¤ects on e( i ) for both the cognitive and non-cognitive occupations. This means that P k does not a¤ect the comparative advantage for non-cognitive human capital. We now plug the worker’optimal choice in (6) into her maximization problem, and obtain the following expression for her highest net income in occupation i Ii ("i ) = (1
)
1
wik k k h " Pk i i
1 1
(7)
Equation (6) and (7) show that net income, Ii ("i ), is proportional to educational spending, ei ("i ). This result will be handy for our analyses below. In addition, equation (7) implies that the worker chooses occupation n if and only if wck hkc "kc wnk hkn "kn . This is a classic discrete-choice problem (e.g. McFadden 1974). Using the Frechet distribution (1) we show, in the Appendix, that Proposition 1 The employment share of occupation i equals pki =
Ti (wik hki ) , i = c; n: Tc (wck hkc ) + Tn (wnk hkn )
(8)
Equation (8) says that the non-cognitive employment share, pkn , is high, if workers have a strong comparative advantage in non-cognitive innate abilities (high Tn =Tc ), noncognitive skills have a high relative return in the labor market (high wnk =wck ), or country k has a strong comparative advantage in fostering non-cognitive human capital (high hkn =hkc ). In (8), plays an important role. As rises and workers become more homogeneous, given changes in wik or hki lead to bigger shifts in the proportion of workers that opt to work in di¤erent occupations. Equation (8) characterizes individuals’ optimal choices for the types of human capital accumulated, and plays a key role in our model. To solve the model, we start by calculating the average net income of non-cognitive and cognitive workers, which analytically involves taking the expected value of equation (7), with respect to "i , conditional on type i, i = n; c. We show, in the Appendix, that 14
Proposition 2 The average net income is the same for non-cognitive and cognitive workers; i.e. " # (11 ) k k w w c k n k Tc Ink = Ick = (1 ) 1 h h ; (9) + Tn Pk c Pk n where
=
(1
(1
1 )(1
)
)
Proposition 2 is a common feature of the solution to discrete choice problems where the underlying distribution is Frechet (e.g. Eaton and Kortum 2002). In equation (8), the term in the square brackets is the denominator of the employment-share expression, (8). (:) is the Gamma function and so is a constant. Proposition 2, together with equations Corollary 1 The average educational expenditure is the same for non-cognitive and cognitive workers and is equal to
Enk = Eck =
2 4
Tc
wck k h Pk c
+ Tn
wnk k h Pk n
!1 31 5
1
(10)
By the Corollary we now use E k , without an occupation subscript, to denote the average educational spending in country k. Proposition 2 and its corollary will prove useful in pinning down , the elasticity of the output of human capital with respect to input, as we show in section 4. Finally, we de…ne the local supply of e¤ective labor of type i as LkS i . We show in the Appendix that Proposition 3 Given occupational and educational choices of workers, the aggregate supply of locally provided labor of type i in country k is 0 !1 111 k k k k L pi @ wn k wc k k k k A LkS h + T h Tc : (11) n i = L pi E(hi e jOccp:i) = c k Pk Pk n wi To complete our characterization of labor supply, we use equations (8) and (11) to derive the relative supply of non-cognitive labor, which is given by Tn LkS n = kS Lc Tc
hkn hkc 15
wnk wck
1
(12)
kS Intuitively, the relative supply of non-cognitive labor, LkS n =Lc , is increasing in the availability of raw talent in the country, the comparative advantage of that country in noncognitive human capital, hkn =hkc , and the relative return of non-cognitive human capital, wnk =wck . As foreshadowed by our discussion of Proposition 1, it is clear from equation (12) that is the supply elasticity: as workers’skills become more homogeneous, a given change in hkn =hkc or wnk =wck a¤ects the occupational choices of more workers, and so solicits kS in section 4 below. a larger response in LkS n =Lc . We will obtain the value of k k k k k k Finally, equation (11), together with wc Lc + wn Ln = P y , implies that the income share of cognitive workers in the population is given by
wik LkS i = pki : P k yk
(13)
This completes the labor supply side of the model. We now turn our attention to the demand side. Cost minimization by …nal goods producers facing technology (4) determines the demand for cognitive and non-cognitive labor. The …rst order conditions imply that the relative demand for non-cognitive labor is given by LkD Ac wnk n = (14) LkD An wck c Equation (14) is a standard relative demand equation where the key demand elasticity is given by . Cost minimization using equation (4) also implies that the cost share of labor input of type i in country k is given by) ski
=
Ai wik Ac (wck )1
1
+ An (wnk )1
:
(15)
kS We now use (13) and (15) to show that the aggregate supplies, LkS c and Ln , di¤er from aggregate demand, LkD and LkD c n , by international trade. We de…ne GDP-normalized net exports of type i human capital as
nxki =
wik LkS LkD i i = pki P k yk
ski
(16)
Equation (16) makes it clear that if ski > pki country k must be a net importer of type i human capital. With balance-of-trade, nxkc + nxkn = 0. In order to relate the aggregate quantities of cognitive and non-cognitive human capital to trade and occupation 16
employment shares, it is convenient to de…ne net exports as ratios xki =
LkS LkD nxki i i = ; i = c; n LkS pki i
(17)
For example, if xkc = 0:5%, country k imports cognitive human capital, the quantity of which is 0.5% of its aggregate supply. Using equations (12)-(17), we have LkD n = LkD c
Ac An
1
pkn pkc
1
1 ( 1
xkn ) xkc
1 1
(18)
We can think about the intuition of equation (18) in two steps. First, assume that there is no trade; i.e. xkn = xkc = 0. Equation (18) says that if we observe, in the data, that many in country k choose the non-cognitive occupation (i.e. pkn is high and pkc low), we can make the inference that country k has a large relative quantity of non-cognitive human capital. With international trade, some of country k’s residents sell their services abroad in exchange for imports of the services of other countries’residents, and the last term of equation (18) shows us how to make adjustments to pkn and pkc , which show the employment shares of country k’s residents. We can also relate the relative returns for human capital to occupation employment shares and trade. Working with equations (12)-(16) and making use of the trade balance condition, we have 1 1 1 wck Ac pkn nxkn = : (19) wnk An pkc nxkc To see the intuition of equation (19), we again start with autarky; i.e. nxkc = nxkn = 0. In this case, (19) says that the relative factor return, wck =wnk , is inversely related to relative factor abundance, which can be measured by pkc =pkn according to equation (18). With international trade, then, (19) says that this autarky relationship should be adjusted accordingly. The more trade there is, the larger are the magnitudes of nxkc and nxkn , and the more we deviate from the autarky relationship between wck =wnk and pkc =pkn .17 Equations (18)-(19) will prove useful in allowing us to back out cognitive and noncognitive productivities from the data. Below, we will further close the model for two special cases: autarky and free trade. For now, we do not concern ourselves with the international market clearing but turn instead to demonstrating how educational productivities can be measured. 17
Under free trade, wck =wnk is independent of country k’s occupation employment shares because it is equalized for all countries.
17
3.3
Output per Worker, Aggregate Educational Quality and Output TFP
Our model delivers an analytical expression, decomposing country income di¤erences into a component that re‡ects pure educational productivity, and a residual that re‡ects other sources of country productivity di¤erences. To do so, we …rst de…ne a base country 0 against which any particular country can be compared. We show, in the Appendix, that output per worker in country k relative to the base country 0 is 3 2 0 0 1 11 1 ! 1 1 0 0 k 1 y k =Lk 6 p0c nx0c hkc hkn A C 7 B 0 0 @ pn + nxc 6 = + p p @ A 7 c n 5 (20) y 0 =L0 4 0 pkc nxkc h0c pkn + nxkc h0n To show the intuition of equation (20), we consider the special cases of autarky and free trade.
Special Case: Closed Economy In this case, equation (20) simpli…es to (see the Appendix for the details) y k =Lk = y 0 =L0 where k
0
@p0c
hkc h0c
1
k
1
k
1
(21)
1
0
(
1)
+ 1=(1
p0n )
hkn h0n
(
1)
1 A
(
1)
(22)
The …rst term in equation (21), k = 0 , is the variation across countries in their output per worker that is due to Hick’s neutral productivity di¤erences. The sources of these di¤erences could be associated with many factors, such as e¢ cient court systems and business regulations. Note that because higher output TFP lowers the relative price of the …nal good and makes it easier to produce human capital, its e¤ect on output per worker is ampli…ed by the power 1=(1 ). k 1=(1 ) The second term, [ ] , is the portion of per capita income di¤erences across k countries that is due to , the overall education quality. k is a weighted power mean of the cognitive and non-cognitive productivities, with the weights being the occupational employment shares of the base country. This measure is akin to an index, summarizing 18
the multi-dimensional di¤erences in cognitive and non-cognitive productivities into a single numerical value, and it captures the contribution of the overall quality of the educational institution to output per capita. Because the powers in k are determined by the demand and supply elasticities, and , they play important roles in determining how overall education quality, k , relates to cognitive and non-cognitive productivities, hkc and hkn . As both , ! 1, k goes to the maximum of hkc and hkn . This is intuitive, as workers become equally capable at both perfectly substitutable tasks. In this case, being strong in producing one type of human capital but weak in producing the other type has few consequences for a country’s well-being. As ! 1, however, the aggregate production function becomes Leontief, k goes to the minimum of hkc and hkn , and excelling along a single dimension in human-capital production does little good for national well-being. For the more empirically relevant case found in our data (see below) k is reasonably well approximated as a geometric mean. In this case, the relative importance of cognitive and non-cognitive productivities is determined by the occupational shares.18 Special Case: Free Trade In the case of free trade, all countries produce …nal output using the same mixture of resources but are free to specialize in the occupation types in which they excel., i.e. there must be a single global price per unit of cognitive (wc ) and non-cognitive (wn ) human capital. Given e¤ective factor price equalization, it immediately follows that there is a common numeraire for all countries can be de…ned. It is useful to de…ne this numeraire as a bundle of inputs into …nal production, i.e. 1 1 = 1, and that the price of …nal output in country k (Ac ) (wc )1 + (An ) (wn )1 1 k k is given by P = . In this case, equation (20) simpli…es to (see the Appendix for the details)
y k =Lk = y 0 =L0 where
k
=
1
k k 0
p0c
hkc h0c
18
1
(23)
; + p0n
hkn h0n
!1
(24)
Note that the less substitutable are the two types of skills in the population (smaller ) the bigger the penalty toward poor performance in just one of the dimensions of human-capital investments.
19
Comparing the free-trade decomposition with that of the closed economy given by equation (21), we see that the key di¤erence is in the power coe¢ cients in the construction of the power mean of cognitive and non-cognitive productivities. Critically, the power coe¢ cients under free trade do not include as local labor market demand does not have to equal local labor market supply. This has the e¤ect of increasing the size of these power coe¢ cients. Under the condition that > 1, it is as if ! 1 in the closed economy case and so being relatively ine¢ cient at producing one type of human capital is less of a drag on output per worker. Intuitively, in a world of free trade the ability to buy rather than make the comparative disadvantage good is a source of welfare gains. Our analysis here demonstrates that the implications of an educational system that is weak along one dimension are more severe for a country in autarky relative to one that enjoys international trade in factor content. As we show below, the case of autarky is a much better approximation to the global equilibrium compared to one of free trade.
3.4
Cognitive and Non-cognitive Productivities: Meaurement
We begin by backing out a country’s comparative advantage in human capital production from data. Rearranging equation (8) we can solve for a country’s relative human capital accumulation productivities: 1 pkc =Tc wnk hkc = : hkn pkn =Tn wck Intuitively, if a large fraction of the population is employed in cognitive occupations despite a low relative wage in that occupation, it must be that accumulating cognitive human capital is relatively easy. Now, substituting for relative wages using (19), and dividing country k’s expression relative to a base country 0, we obtain hkc =hkn = h0c =h0n
pkc =pkn p0c =p0n
1
+
1 1
1
fk f0
1
; fk =
1 1
xkc xkn
(25)
To see the intuition of equation (25), we start with autarky, when it simpli…es to pkc =pkn = p0c =p0n
hkc =hkn h0c =h0n
(
1)
;
(26)
where + 1 > 0. Equation (26) shows the importance of the key demandside elasticity, . Suppose hkc =hkn increases; i.e. country k has a stronger comparative 20
advantage in producing cognitive human capital. By equation (8), this has a direct e¤ect on the relative employment share of cognitive occupations, pkc =pkn , as well as an indirect e¤ect on it, through the movement of the relative return to cognitive human capital, wck =wnk . Equation (26) says that the net e¤ect depends on . If > 1, demand is elastic, and so the movement in the relative return is small, and the direct e¤ect dominates. Therefore, a larger relative employment share of cognitive occupations re‡ects a greater comparative advantage for cognitive human capital. When 1, however, this result does not hold. We show, in section 4 below, that data indicates > 1. We now go back to equation (25). It has the ‡avor of revealed comparative advantage: we can back out a country’s comparative advantage for cognitive human capital, the lefthand side of (25), using the data and parameter values on the right-hand side of (25). The …rst term there captures the e¤ects of the endogenous choices of workers and the optimal hiring decisions of the …nal goods producers. If we observe, in the data, that many have chosen the cognitive occupation in country k, we can infer that country k has a strong comparative advantage for cognitive human capital, with > 1. The second term on the right-hand side of (25) captures the e¤ects of international trade. With > 1, if we observe, in the data, that country k imports, in the net, the service of cognitive human capital (i.e. xkc < 0), we can infer that country k has a stronger comparative advantage for cognitive human capital than its employment shares suggest, because the cognitive workers in k have chosen their occupation despite import competition. We now turn to backing out a country’s absolute advantage in producing human capital from data. To do this, we assume that country k’s average score on international exams, such as PISA, is informative about its aggregate supply of cognitive human capital. Country k’s cognitive productivity can then be obtained by appropriately adjusting this test score for educational expenditures and occupational choices. Speci…cally, for some positive constant b, we assume that Sk = b
LkS c ; Lk
(27)
k k k k k where LkS c is given by (11). Proposition 2 implies that wc Lc = pc Py y , which together with (8) and (10), can be combined to yield the following expression for country k’s cognitive human capital accumulation productivity relative to a base country:
Sk = S0
Ek E0
pkc p0c 21
1
1
hkc h0c
(28)
As expression (28) makes clear, a good showing on international tests can happen for multiple reasons. First, a high test score could be obtained by a high level of spending on education per capita, E k . The e¤ect of E k on cognitive human capital, and so test score, is raised to the power of , because the production technology of human capital, (2), is subject to diminishing returns. The second term in (28) captures the e¤ects of incentives and selection, and they arise in general equilibrium because heterogeneous individuals make optimal choices for human capital investment. To see these e¤ects, suppose pkc is high in country k; i.e. a larger fraction of the labor force favors the cognitive occupation over the noncognitive occupation. This could be because the relative return to cognitive skills in country k, wck =wnk , is high, or country k has a strong comparative advantage in fostering cognitive human capital (i.e. hkc =hkn is high). In either case, the cognitive occupation is an attractive career choice in country k, and so individuals have strong incentives to accumulate cognitive human capital. This incentive e¤ect implies high average test score for country k, and its magnitude is raised to the power of 1. On the other hand, workers are heterogeneous, and so a high pkc implies that many individuals with low innate cognitive abilities have self-selected into the cognitive occupation. Their presence tends to lower the average cognitive human capital, and so the test score. The magnitude of this selection e¤ect is pkc raised to the power of 1= . If is large, the distribution of innate abilities becomes more compressed. This means less individual heterogeneity and so the selection e¤ect is weaker. Note that because > 1 the incentive e¤ect always dominates. We allow the data to steer us to the most appropriate value for , and it will turn out that the value does indeed exceed one. Finally, cognitive productivity, hkc , soaks up all the other reasons why the test score is high for country k, net of the e¤ects of resources, and incentives minus selection. In this sense, hkc is country k’s TFP in producing cognitive human capital. An important implication of equation (28) is that, in order to isolate hkc , one has to adjust test scores for the convoluting factors of educational expenditures and occupational employment shares.
22
4
Values of Structural Parameters
As we have shown in the previous section, given the elasticities, , , and , and data Lk , labor-force size, yk , aggregate output, pkn , non-cognitive employment share, and pkc , cognitive employment share by country, we can extract the values of …nal-good TFP, k , and the TFPs of human capital production, hkn and hkc . As these data are readily available, the challenge is to obtain the values of these elasticities. Speci…cally, our data includes labor force by cognitive and non-cognitive occupation, international test scores, real GDP per capita, and the cognitive and non-cognitive factor content of trade. Descriptive statistics are shown in Table 2.
4.1
Elasticity of Human Capital Production,
We begin with , the elasticity of human capital attainment with respect to educational expenditure. Corollary 1 and Proposition 3 imply that Proposition 4 Country k spends fraction
of its aggregate output on education; i.e.
E k Lk = y k .
(29)
P k P k k k k p = Proof. By equations (9) and (10), wik Lki = Lk pki E k = , and so i wi Li = L E P k k i i k k E L . In our model aggregate output equals aggregate income, and so i wi Li = yk . By equation (29), is the ratio of aggregate educational spending, E k Lk , to aggregate output, yk . Therefore, we set its value to match the mean share of public plus private educational expenditure in output, 0.1255 (see Table 2); i.e. = 0:1255.
4.2
Supply Elasticity,
We now turn to , which measures the dispersion of innate abilities across workers and also governs the elasticity of the aggregate supplies of human capital. Using the results of the previous proposition and equation (28), we obtain ln
Sk (y k =lk )
=D+ 1
23
1
ln pkc + ln hkc
(30)
where D is a constant. Equation (30) decomposes the cross-country variation in the average test score, S k , into resource inputs, (y k =Lk ) , incentives (minus selection), pkc , and cognitive productivity, hkc .19 Equation (30) also instructs us to construct variables and to look for novel correlation patterns that previous research has not examined. We follow these instructions in Figure 2. The vertical axis is log PISA math score, normalized by the logarithm of output per worker raised to the power of . The horizontal axis is log cognitive employment share. We weigh the data in the scatterplot using aggregate output.20 Figure 2 clearly illustrates that, consistent with equation (30), the countries in which workers are clustered in cognitive occupations are the countries that score well on tests (normalized by resources inputs), which can measure primarily cognitive achievement. The best-…t line has R2 = 0.288 and a slope coe¢ cient of 0.717. This novel correlation pattern provides an important validation that incentives indeed matter for the accumulation of human capital, a key mechanism of our general-equilibrium model. Figure 2 also allows us to interpret the correlation pattern as structural parameters of our model, because it follows the exact speci…cation of equation (30). The slope coe¢ cient of the best-…t line corresponds to the coe¢ cient of log cognitive employment share, 1 1 , implying that = 3:4965. This estimate for provides yet another validation of our model, which, as we discussed in section 3, requires > 1. The countries’deviations from the best-…t line then correspond to the log of their cognitive productivities, hkc . Furthermore, Figure 2 illustrates the intuition for the identi…cation of . As we discussed earlier, with individual heterogeneity, selection moderates the e¤ect of incentives on average cognitive human capital. A small implies high heterogeneity and strong selection e¤ect. This means we should observe limited variation in the normalized test scores despite substantial variation in cognitive employment shares; i.e. log cognitive employment share should have a small slope coe¢ cient in Figure 2. Therefore, we identify through the strength of the selection e¤ect, the magnitude of which is 1= according to our model. Table 5 shows the results of …tting our data using (30), implemented as a regression 19
Relative to (27), (30) has output per worker rather than educational expenditure per worker, because we have more data points on output per worker than for average educational expenditure per capita. 20 The countries in our sample vary a lot in their size (e.g. Switzerland, Germany, and the United States.)
24
with aggregate output as weight. Column (1) corresponds to the best-…t line in Figure 2. In column (2) we add Australia and New Zealand but dummy them out,21 and in column (3) we use labor-force size as weight. The results are very similar to column (1). In column (4) we use PISA reading score. The coe¢ cient becomes smaller, 0.521, and remains signi…cant, implying that = 2:0877. Column (5) has PISA science score and the results are similar to column (4). Column (6) uses the O*NET characteristic of enterprising skills as an alternative measure of leadership, and so non-cognitive occupations. The coe¢ cient is positive but not signi…cant, and this pattern echoes column (3) of Table 2.22 Table 5 produces a range of values for , 2:0877 ~3:4965. We use = 3:4965 in the rest of the paper and show below that our estimates are very similar to the literature, and that we get very similar results if we use other values for (e.g. 2:0877) instead. We then calculate the residuals and construct cognitive productivities, hkc , according to (30). Like the output-TFP estimates in the macro literature (e.g. Hall and Jones, 1999), our estimates for cognitive productivities are relative, and so we normalize the U.S. value to 1.
4.3
Demand Elasticity,
For the value of , the substitution elasticity on the demand side, we turn to the aggregate production function (4). Speci…cally, we substitute out the quantities of human capital, Lkc and Lkn , using the …rst order conditions for …nal good producer pro…t maximization, and equations (19), (27) and (??). After some algebra, we obtain log
yk 1 k k S L 1 xkc
=F+
1
log 1 +
pkn pkc
nxkn nxkc
+ log
k
(31)
where the constant F has no cross-country variation. Equation (31) is an input-output relationship. The output is y k , and there are two inputs. The …rst is the quantity of cognitive human capital, represented by Lk S k , since test score, S k , represents average cognitive human capital of country k’s residents by equation (27). We adjust it by 1 xkc to take into account net export of the services of cognitive human capital. The second input is the relative quantity of non-cognitive 21
As discussed in subsection 2.2, these countries have di¤erent occupation classi…cation codes in their raw data. 22 We present the results of alternative measures of non-cogntivie occupations in Appendix Table 4A.
25
k
k
k
pn n human capital used in production, ppnk nx k , where pk re‡ects the relative quantity of c nxc c country k’s residents and so we adjust it by nxkc and nxkn to take into account trade in the services of human capital. Therefore, equation (31) shows how aggregate output, normalized by the quantity of cognitive human capital, varies with the relative quantity of non-cognitive human capital, and this variation identi…es . The estimation of (31), then, is similar to the estimation of the aggregate production k nxk n gives us , and the residuals give us k , function.23 The coe¢ cient of log 1 + ppnk nx k c c the output TFP. In the estimation, our data disciplines our model for two reasons. First, (31) instructs us to use the average test score as one input and the ratio of employment shares as the relative quantity of another input. These are novel ways to measure the quantities of human capital that previous research has not considered. Table 6 shows the results of …tting our data using (31), implemented as a regression with aggregate output as weight. The structure of Table 5 is similar to Table 4 and so are the ‡avors of the results. Columns (1), (4) and (5) use PISA math, reading and science scores, respectively. Column (2) drops Austalia and New Zealand, and column (3) uses labor-force size as weight. The coe¢ cients are all signi…cant, ranging from 2.923 to 3.125. Using 3.125 we infer that = 1:505. Column (6) uses enterprising skills as the alternative measure for non-cognitive occupations, and the coe¢ cient is positive but not signi…cant, echoing Tables 2 and 4. In column (7), we consider the case of autarky, setting xkc = nxkn = nxkn = 0 in (31). The results are very similar to column (1). We then calculate the residuals and construct the output TFP, k , according to (31), normalizing the U.S. value to 1. We check the correlation coe¢ cients between our output TFP estimates and those reported in the literature. They are all positive and signi…cant, ranging from 0.4674 (Klenow and Rodriguez-Clare 1997) to 0.6377 (PWT 8.0), and provide an external validation for our approach.24 23
As in the macro literature, we implicitly assume that output TFP is uncorrelated with relative quantity, which in our case is determined by the comparative advantage of human capital production. While progress has been made in the micro literature with respect to identi…cation, it has been slower in the cross-country macro literature. 24 See Appendix Table A4 for all the pairwise correlation coe¢ cients.
26
5
Cognitive and Non-cognitive Productivities
The elasticities estimated in the previous section combined with the data and equations (25) and (28) imply the full set of values of hkc and hkn . In this section we present the estimates.
5.1
Cognitive Productivity
Figure 3 plots the countries’rankings in hkc against their rankings in PISA math score, and Table 3 lists these rankings by country. These two rankings are positively correlated (0.5101), since both test score and cognitive productivity measure the quality of human capital production along the cognitive dimension. However, Figure 3 shows that they are quite di¤erent for many countries. We highlight these di¤erences using the 45 degree line. These di¤erences arise because test score is an outcome, and so a noisy measure for the underlying quality of cognitive-human-capital production. Equation (30) highlights two sources of noisiness. The …rst is resources, (y k =Lk ) . Other things equal, a country with more resources inputs is expected to produce better outcome. The second is incentives (minus selection), 1 1 ln pkc . The country where individuals are strongly incentivized to learn cognitive skills will perform well in international tests. Equation (30) then allows us to use test score, S k , as the starting point, and remove the e¤ects of resources and incentives, to arrive at our cognitive productivity, hkc . Therefore, cognitive productivity is a cleaner measure for the underlying quality of cognitive education than test score. Consider, …rst, Poland, Czech Republic, Hungary and Slovakia. They have decent PISA scores, ranked outside of top 10. However, our model says that this outcome should be viewed in the context of low output per worker in these countries, and so limited resources for human capital production. Therefore, the qualities of their educational institutions are better than their test scores suggest, and they all rank within top 10 based on cognitive productivities. Now consider Hong Kong, South Korea and Switzerland. They are superstars in PISA scores, all ranked within top 5. However, our model says that this outcome should be viewed in the context of high cognitive employment shares and so strong incentives to accumulate cognitive human capital. Therefore, the qualities of their educational institutions are not as good as their test scores suggest, and their rankings drop to 10, 27
12 and 14, respectively, by cognitive productivities. Finally, we look at the U.S. First, the U.S. has very high output per worker. The abundance of resources makes the low U.S. PISA scores even harder to justify. Second, the employment share of cognitive occupations is relatively low in the U.S., implying weak incentives to accumulate cognitive human capital. The e¤ects of resources and incentives thus o¤set each other, leaving the U.S. ranking in cognitive productivities very close to its ranking in PISA scores, near the bottom in our set of 28 countries. In our Introduction, we discussed the worries and concerns about the quality of the U.S. educational system. Figure 3 quanti…es these concerns and shows that they are well justi…ed, when we look at the cognitive dimension. We now move on to the non-cognitive dimension.
5.2
Non-cognitive Productivity
Figure 4 plots the countries’rankings in hkn against their rankings in PISA math score, and Table 3 lists the rankings by country. Figure 4 clearly shows that the PISA-math rankings are simply not informative about non-cognitive productivity rankings (correlation = 0:0602 with p-value = 0:7609). Thus non-cognitive productivities allow us to compare countries’educational systems in a novel dimension, hidden from PISA scores. In our Introduction, we discussed the concerns in S. Korea and many East Asian countries that the educational systems emphasize exams so much that students are unable to develop non-cognitive skills. Our results in Figure 4 quantify this issue and suggest that these concerns are well grounded. S. Korea and Hong Kong, super starts in terms of PISA scores, round up the very bottom among our 28 countries. They have low non-cognitive productivities for two reasons. First, they have decent, but not stellar, cognitive productivities, as shown in Figure 3. In addition, in these countries, many choose the cognitive occupations, implying that these countries have weak comparative advantages for non-cognitive human capital, by equation (25). Figure 4 also shows that PISA-math rankings substantially understate the pro…ciency of the U.S. and U.K. in fostering non-cognitive skills. The U.S. ranks in the middle of our 28 countries and the U.K. ranks No. 4. Many in the U.S. have long argued against focusing exclusively on test scores in education.25 Figure 4 provides quanti…cations for 25
For example, the National Education Association states that, in response to NCLB and RTT, “We see schools across America dropping physical education . . . dropping music . . . dropping their arts
28
this argument, showing that the U.S. indeed has a comparative advantage for noncognitive skills. As for the U.K., it ranks ahead of Hong Kong in both non-cognitive (Figure 4) and cognitive productivities (Figure 3), and it seems reasonable to assume that Hong Kong and Shanghai, China, have similar educational systems. If the former U.K. education minister, Elizabeth Truss, had known about these rankings in 2014, would she have traveled to Shanghai to “learn a lesson in math”? In summary, our estimates for cognitive and non-cognitive productivities provide better numerical metrics than test scores for the qualities of education. As another example, Figures 3 and 4 suggest that the educational systems of Finland, Netherlands and Belgium are far more worthy of emulation than those of South Korea and Hong Kong. Below we condense the multi-dimensional di¤erences in cognitive and non-cognitive productivities into a single index for the overall educational quality, and quantify its contribution to output per worker.
5.3
Aggregate Educational Quality
In this section, we present decompositions of output per worker across countries into a component that is due to pure TFP di¤erences ( k in the model) and to the quality of a country’s educational system ( k ). We present three sets of decompositions. The …rst are the estimates that follow directly from the model that accounts for observed levels of factor content trade.26 The second is the case of the closed economy where the net factor content of trade is constrained to be zero. Finally, we consider the case of free trade in which factor prices wck and wnk are constrained to be the same everywhere. In each set of calculations, we re-estimate hkc and hkn to be consistent with the assumed degree of tradability. The results are shown in Table 8. The …rst column of table 8 shows the actual level k k ). Columns 2 and of GDP per capita by country relative to the United States (i.e. yy0 =L =L0 h k i11 1 3 correspond to estimates of TFP, 0 , and of educational quality, k 1 , implied by observed factor content of trade. Columns 4 and 5 correspond to estimates obtained under the assumption of no factor content trade, and columns 6 and 7 correspond to the programs . . . all in pursuit of higher test scores. This is not good education.” 26 In this case, there is no clean decomposition of the quality of educational system in a closed form that presents the relative contributions of hkc and hkn . A mixture of data hkc and hkn estimates allow the calculation t be made, however.
29
case of free trade in factor content. There are several messages to be gleaned from the estimates in table 8. First, the productivities estimated in columns 2 and 3 suggest large variation across countries in terms of both eduactional quality and TFP. To interpret the estimates, consider Germany. The overall quality of Germany’s educational institution is lower than the U.S., the e¤ect of which puts Germany’s output per worker at 88.34% of the U.S. level (column (3)). On top of this, Germany also has lower output TFP than the U.S., the e¤ect of which places its output per worker at 71.26% of the U.S. level (column (2)). Aggregating these two e¤ects, Germany’s output per worker is 62.96% (= 88.34% x 71.26%) of the U.S. level (column (1)).27 Now consider the large di¤erences in overall educational qualities across countries. For example, columns 2 and 3 show that although S. Korea’s educational system delivers high test scores, it puts S. Korea’s output per worker at 71.42% of the U.S. level, other things equal. Finland, on the other hand, has the strongest educational institution in our sample, which puts Finland’s output per worker at 154.58% of the U.S. level, ceteris paribus. These results suggest that educational policies and reforms have very large potential payo¤s, as well as danger, in terms of aggregate output.28 Second, columns 3 and 5 are very close in terms of their estimates. This tells us that the closed economy model is a very good approximation for the actual estimates. This is because the observed level of factor content of trade relative to occupational choice di¤erences across countries is very small. Hence, the educational productivities for cognitive and non-cognitive human capital accumulation that have been estimated taking into account factor content trade are very close to those that would obtain in a closed economy. A nice feature of the decomposition for the case of autarky is that it allows us to plot k hc and hkn for the countries in our sample to understand why the rankings appear in table 8 as they do. We do this in …gure 5. The line that passes through the United States in this diagram is what we call an iso-education-quality curve. These are the combinations 27
Columns (2) and (3) in Table 8 are based on = 3:4965 and = 1:4706. Table 7 shows that we obtain very similar values and country rankings for overall education quality under alternative values of and . 28 The countries’rankings in overall education quality are very similar to their rankings in non-cognitive productivity (correlation is 0:9425). The correlation between overall-education-quality rankings and PISA-math rankings is 0:0909 (p value = 0:6456).
30
of hkc and hkn that yield a constant level of educational quality . As it pass through the United States, we can see which countries fair better and which worse while the curvature of the curve tells us about the trade o¤s of increasing cognitive educational productivity for non-cognitive educational productivity. It also illustrates the countries whose overall education qualities are similar to the U.S. (e.g. Sweden and Denmark), those with higher overall education qualities than the U.S. (e.g. the U.K. and Finland), and those with lower overall education qualities (e.g. Italy and S. Korea). We see that although Korea and Hong Kong excel in earning high test scores, the imbalance of their productivities hold back their overall performance. There is, however, a silver lining: this imbalance would be a very useful asset under free trade, as we show in section 6.2.
5.4 5.4.1
Extensions and Robustness Parameter Values
We …rst compare our parameter values with the literature. Hsieh et al (2016)’s model features the same Frechet distribution of innate abilities as ours, but for identi…cation they use worker-level data and explore wage dispersion within occupations and laborforce participation; i.e. their data and identi…cation strategy are completely di¤erent from ours. Despite such di¤erences, Hsieh et al (2016)’s estimate ranges from 2:1 to 4, matching our range of 2:0877 to 3:4965. On the other hand, Burnstein et al. (2016) features a CES aggregate production function, like us, but for identi…cation they use cross-section and over-time variations in occupational wages and employment in micro data. Although Burnstein et al. (2016)’s data and identi…cation strategy are completely di¤erent from ours, their substitution-elasticity estimate ranges from 1:78 to 2, similar to our value of 1:4706.29 We now perform sensitivity analyses. We …rst use = 2:0877 and PISA reading scores to obtain cognitive and non-cognitive productivities and rank countries using these alternative values. We then calculate the correlation coe¢ cients of these alternative values and rankings with our main closed-economy speci…cation, and report them in the second row of Table 9. We next consider = 2:0877 and = 2 under the closedeconomy setting, and report the correlation coe¢ cients in the third row of Table 9. These 29
The substitution-elasticity parameter is not identi…ed in Hsieh et al. (2016). Burnstein et al. (2016), on the other hand, do not model the production of human capital.
31
correlation coe¢ cients range from 0:9583 to 1:0000. Finally, we specify = 2:0877 for the setting of free trade, and obtain correlation coe¢ cients ranging from 0:8058 to 0:9562, as shown in the last row of Table 9. To summarize, we obtain similar values and rankings of cognitive and non-cognitive productivities under alternative parameter values and the alternative setting of free trade. 5.4.2
Middle-Income Countries
In this sub-section we extend our sample to also include the middle-income countries that have 3- or 4-digit ISCO-88 occupation data. This increases the number of countries we have from 28 to 34. We focus on the results under the closed-economy setting, to keep our discussions succinct. Figure 6 plots normalized PISA math score against the log of cognitive employment share for our extended sample. It is similar to Figure 2. Column (7) of Table 4 shows the implementation of equation (30) using the extended sample. The results are similar to column (2), implying that we obtain similar values for and hkc for the extended sample. Column (8) of Table 5 show the implementation of equation (31) using the extended sample. The results are similar to column (1), indicating that we obtain similar values for and k , and so hkn , for the extended sample. To help visualize these similarities, we use these parameter values of the extended sample to graph the iso-education-quality curve in Figure 6. We label the names of the middle-income countries in all capital letters. Figure 6 is similar to Figure 5. It also enriches Figure 5, showing that overall education quality varies substantially among the middle-income countries.
6
Comparative Statics
As dataset does not include information for many of the world’s largest countries (e.g. China, India, Indonesia...), a credible counterfactual exercise is unlikely to prove very illuminating. However, as the data suggest that autarky is a reasonable approximation for global factor trade, it is reasonable to conduct some calculations under the assumption that economies are closed. We make several such calculations for shifts in educational priorities to explore the economic tradeo¤s. In addition we conduct an alternate exercise to illustrate how greater trade might in‡uence the relative qualities of di¤erent educational systems. To do this, we take the 32
educational productivities estimated in section 4 and imagine that they were generated by a world in which trade in intermediate was perfectly frictionless between countries. Then, using the free trade decomposition given by equation (23), we can get an idea of how trade would e¤ect the tradeo¤s facing policymakers.
6.1
Closed Economy
We now calculate how changes in the qualities of the educational institution a¤ect test scores and aggregate output for any country k, and how such calculations help inform the discussions of education policies and reforms. These comparative statics are very easy to implement using our model. First, equations (21) and (22) provide closed form solutions for output per worker, and map changes in educational TFPs into changes in output per worker relative to any arbitrary base country 0. This "country 0" in our model can be speci…ed as the initial equilibrium of country k itself. On the other hand, equations (26), (29) and (30), together with the identity pkc + pkn = 1, imply that the change in test score is a log-linear function of the changes in cognitive and non-cognitive productivities (see the Appendix for the proof) (1
)d ln S k = (1 + Bpkc )d ln hkc
(Bpkn )d ln hkn ; B =
(
1)( +
1) 1
> 0;
(32)
where B = 0:2496 according to our parameter values.30 Equation (32) says that an increase in test score, S k , can be achieved by either an increase in cognitive productivity, hkc , and/or a reduction in non-cognitive productivity, hkn . The latter works because an educational institution with a very low level of non-cognitive productivity simply denies most people the option of accumulating non-cognitive human capital. This creates very strong incentives to accumulate cognitive human capital, showing up as an increase in test score. As a result, a rise in test score may result from a better educational institution along the cognitive dimension, or a worse one along the non-cognitive dimension. While the former is a blessing, the latter is a curse in disguise, as we illustrate below. Suppose the U.S. can implement some policy reform to boost its PISA score by 2.58%, in order to advance 5 places in PISA math rankings. This puts U.S. PISA math score at U.K’s level. To illustrate the intended consequence of this policy, assume that U.S. non-cognitive productivity, hUn S , remains unchanged. Equation (32) tells us that U.S. 30
This is based on
= 3:4965. If
= 2:0877, B = 0:1279.
33
cognitive productivity rises by 2.12%, and equation (21) tells us that U.S. aggregate output rises by 1.81%. The increase in output provides an upper bound estimate for the amount of resources to be spent on the reform, or an estimate for the potential returns of the reform if we know the amount of resources spent. This exercise illustrates that our model is a useful tool for the cost-bene…t analysis of education policies. Our model is also useful for clarifying the objective of education policies. In the U.S., both No Child Left Behind of 2001 and Race To the Top of 2009 are motivated by the concern for low test scores, and both measure student performance using test scores. Our model shows that test score and output may move in the opposite direction, because there are multiple types of human capital and heterogeneous individuals respond to policy changes by changing the types of human capital they accumulate. Suppose that the U.S. implements less ambitious education reforms than in scenario 1 above, and succeeds in raising U.S. PISA score by 0.258%. To illustrate the unintended consequence of this policy, assume that U.S. cognitive productivity, hUc S , remains unchanged. Then by equation (32), U.S. non-cognitive productivity, hUn S , decreases by 4.08%, and by equation (21), U.S. aggregate output decreases by 1.02%. This exercise illustrates that an increase in test score could mask a reduction in the overall quality of the educational institution. As a result, aggregate output is a better objective for education policies than test score. Indeed, many educational reforms that are promoted to raise test scores have been criticised because of the fear that improvement along one dimension may come at the expense of decline along another. Our model quanti…es the pros and cons of education policy reforms. For instance, many in the U.S. advocate emulating the heavily test-based educational systems and practices of east Asian countries, such as those in S. Korea and Hong Kong. While this may increase cognitive learning, it can also induce poor performance in non-cognitive human capital. Our calculations in section 4 show that Hong Kong’s cognitive productivity is 1.13 times the U.S. level, but her non-cognitive productivity is 0.40 times the U.S. level. Equation (32) then says that should the U.S. get Hong Kong’s educational system, test score would increase by 22.50%, putting the U.S. as the world champion in PISA scores. However, equations (21) and (22) tell us that despite this accomplishment in test scores, U.S. aggregate output would decrease by 11.13%!
34
6.2
Free Trade Scenario
As we know from the theory, the relative quality of a country’s educational institutions depends on the extent of openness to factor service trade. While the data suggest that the world is closer to autarky than to free trade, it is instructive to see what output per worker would be across countries were international trade frictionless.31 To make this calculation, we use the productivities hkc , hkn , and k in section 4 and the free trade decomposition expression (23) to calculate the implied real output per worker in a world of free trade. As benchmark, we copy column (1) of Table 8 as the 2nd column of Table 10, which shows output per worker relative to the U.S. in the data. Column 3 of Table 10 reports what these ratios would be if there were no friction to trade in the services of human capital, and column 4 calculates the percentage changes between columns 2 and 3. Note that in our model, every country enjoys positive gains from trade, including the U.S. This means that gains from trade exceed the numbers in column 4, because the level of U.S. output per worker would increase in response to trade liberalizations. The results in column 4 show that gains from trade are large; e.g. Germany would gain, at least, 10:70% of its output. To illustrate the intuition for these results, we plot, in Figure 7, the iso-educational-quality curve under free trade. Figure 7 has the same values of cognitive and non-cognitive productivities as Figure 5. However, the isoeducational-quality curve is generated by equation (23) in Figure 7, vs. (22) in Figure 5. As a result, this curve bends sharply towards the origin in Figure 7, in contrast to Figure 5. Figure 7 shows that with free trade, several countries that are exceptional along a single dimension in human capital production would have higher overall education quality than the U.S. The results are highly intuitive: countries that have highly unbalanced educational productivities bene…t dramatically from being able to specialize in the occupations in which they excel. For instance, Hong Kong, S. Korea, and Switzerland, which have a strong comparative advantage in accumulating cognitive human capital, would 31
Our motivations for this world-is-‡at counterfactual are as follows. First, while service trade has been growing faster than goods trade (e.g. wto.org), it has seen less liberalizations than goods trade, and so has more scope for further liberalization. Second, new technology is rapidly decreasing the cost of service trade; e.g. in the U.S., the employment share of contract-…rm workers reaches 14% in 2005 (the Wall Street Journal, A9, Sep. 15, 2007), surpassing the employment share of the manufacturing sector.
35
gain at least 19:61%, 50:63% and 72:24% of their outputs in a world where all trade frictions were to vanish. The Netherlands, which has a strong comparative advantage in accumulating non-cognitive human capital would gain at least 27:24% of its output with free trade. On the other hand, countries with more balanced educational productivities, such as Austria, would see smaller gains from trade.32
7
Conclusion
The measurement of human capital accumulation across countries is fraught with dif…culties. Merely counting the number of students, years of education, or money spent does not correct for quality di¤erences across countries. International test scores o¤er a degree of comparability of student outcomes but su¤er from the fact that they only provide a measure of outcomes along easily codi…ed, cognitive knowledge. Many are concerned that excessive attention paid to test scores not only results in resources that are wasted “teaching to the test” but that students enter the labor market with poorly developed non-cognitive human capital. We adapt the Roy (1951) framework to measure cognitive and non-cognitive productivities of national educational systems and to analyze their importance to in explaining di¤erences in real income per capita across countries. The theoretical framework integrates data on international test scores, educational spending per capita, occupational choices, and international trade. We show that hard to measure non-cognitive human capital is quantitatively important for measuring educational quality. Many countries that perform well on international tests appear to have substandard performance on non-cognitive human capital and this is large enough to drag down their aggregate educational productivity. Our study not only suggests institutional problems in many countries but it also shows that careless attempts to raise performance on international test scores could reduce welfare. While we show that globalization and associated trade in factor services are critical in assessing the quality of a country’s educational institutions, the data suggest that the world is much closer to autarky than it is to free trade. For the moment at least, 32
In our calculations, we assume, for convenience, that the U.S. occupational employment shares are unchanged. We obtain very similar results when we assume, instead, that (1) the U.S. non-cognitive employment share rises by 10%, or (2) falls by 10%.
36
educational institutions that focus on one type of human capital to the great detriment of another are the source of substantially lower income per capita.
References [1] Acemoglu, Daron, Simon Johnson, and James A. Robinson. "The Colonial Origins of Comparative Development: An Empirical Investigation." American Economic Review 91.5 (2001): 1369-1401. [2] Autor, David H., Frank Levy and Richard J. Murname, 2003. “The Skill Content of Recent Technological Change: An Empirical Exploration”, Quarterly Journal of Economics 118(4). [3] Behrman, J. R., Parker, S. W., Todd, P. E., & Wolpin, K. I. (2015). Aligning learning incentives of students and teachers: results from a social experiment in Mexican high schools. Journal of Political Economy, 123(2), 325-364. [4] Burnstein, Ariel, Eduardo Morales and Jonathan Vogel, 2016. “Changes in BetweenGroup Inequality: Computers, Occupations and International Trade”, mimeo. [5] Casselli, F. 2005. “Accounting for Cross-Country Income Di¤erences.”in Handbook of Economic Growth. [6] Choi, Yochul, David Hummels, and Chong Xiang. 2009. “Explaining Import Quality: the Role of the Income Distribution”. Journal of International Economics, 78, 293-303. [7] Cunha, Flavio, James Heckman and Susanne Schennach. “Estimating the Technology of Cognitive and Non-cognitive Skill Formation”, Econometrica 78(3), May 2010, 883-931. [8] Deckle, Jonathan Eaton, and Samuel Kortum. 2008. “Global Rebalancing with Gravity.”International Monetary Fund Sta¤ Papers 55: 511-540 [9] Eaton, Jonathan and Samuel Kortum, 2002. “Technology, Geography and Trade”, Econometrica, 70(5), 1741-1779.
37
[10] Figlio, David and Susanna Loeb, 2011. “School Accountability”, in Handbook of the Economics of Education, Volume 3, Edited by Eric Hanushek, Stephen Machin and Ludger Woessmann, Elsevier North-Holland: Amsterdam, 383-421. [11] Hall, Robert E. and Charles I. Jones, "Why Do Some Countries Produce So Much More Output per Worker than Others?", Quarterly Journal of Economics, February 1999, Vol. 114, pp. 83-116. [12] Hanushek, E., "Education Production Functions", The New Palgrave Dictionary of Economics, 2008. [13] Hanushek, Eric, and Ludger Woessman. 2011. “How Much do Educational Outcomes Matter in OECD Countries?”Economic Policy 26(67): 427-491. [14] Heckman, James J., and Tim Kautz. "Hard evidence on soft skills." Labour economics 19.4 (2012): 451-464. [15] Heckman, James J. and Yona Rubinstein. 2001. “The Importance of Noncognitive Skills: lessons from the GED Testing Program”, American Economic Review Papers & Proceedings 91(2): 145-149. [16] Hsieh, Chang-Tai, Erik Hurst, Charles Jones and Peter Klenow. 2013. “The Allocation of Talent and U.S. Economic Growth”, NBER working paper 18693. [17] Hummels, David, Rasmus Jorgensen, Jakob Munch, and Chong Xiang, 2011, “The wage and employment e¤ects of outsourcing: evidence from Danish matched worker…rm data”, NBER working paper 17496. [18] Hummels, David, Rasmus Jørgensen, Jakob Munch, and Chong Xiang. “The Wage E¤ects of O¤shoring: Evidence from Danish Matched Worker-Firm Data”, American Economic Review, 104 (6), June 2014, 1597-1629. [19] Jones, Benjamin. 2014. “The Human Capital Stock: A Generalized Approach.” American Economic Review 104(11): 3752-3777. [20] Klenow, Peter, and Andres Rodriquez-Clare. 1997. “The Neoclassical Revival in Growth Economics: Has It Gone Too Far?”NBER Working paper.
38
[21] Kuhn, Peter, and Catherine Weinberger. 2005. “Leadership Skills and Wages.”Journal of Labor Economics 23(3): 395-436. [22] Liu, Runjuan and Daniel Tre‡er, 2011. A Sorted Tale of Globalization: White Collar Jobs and the Rise of Service O¤shoring, NBER working paper 17559. [23] Malmberg, Hannes. 2017. “Human Capital and Development Accounting Revisited.”mimeo Institute for International Economic Studies. [24] Neal, Derek A., and William R. Johnson, “The Role of Premarket Factors in Black –White Wage Di¤erences”, Journal of Political Economy 104 (5), October 1966, 869-895. [25] Nunn, Nathan. "Relationship-speci…city, incomplete contracts, and the pattern of trade." The Quarterly Journal of Economics (2007): 569-600. [26] Ohsornge, and Daniel Tre‡er 2007. Journal of Political Economy. [27] Pierce, Justin and Peter Schott, 2009, “A Concordance Between Ten-Digit U.S. Harmonized System Codes and SIC/NAICS Product Classes and Industries”. NBER working paper 15548. [28] Roy, Arthur. 1951. “Some Thoughts on the Distribution of Earnings.”Oxford Economic Papers 3(2): 135-146. [29] Willis, Robert and Sherwin Rosen. “Education and Self-Selection”, Journal of Political Economy 87(5), October 1979, S7-S36.
39
8
Theory Appendix
8.1
Proposition 1
To simplify notation, we drop the superscript k. In addition, let ! c = wc hc , ! n = wn hn , (:) @ 2 F (:) Fc = @F , and F = . Using the de…nition of pn , we have nc @"c @"n @"c Z 1Z 1 pn = Pr(! n "n ! c "c ) = Fnc d"n d"c Z
!c " !n c
0
1
!c Fc ("c ; "n = "c )]d"c !n 0 Z 1 Z 1 !c = Fc ("c ; "n ! 1)d"c Fc ("c ; "n = "c )d"c !n 0 0
=
[Fc ("c ; "n ! 1)
Using the Frechet distribution (1), we have 1
Fc ("c ; "n ) = AF Tc "c (1) When "n ! 1, A = (1
exp[ (Tc "c )1 ][Tc "c
) (Tc "c )
)(Tc )1 "c
(1
) (Tn "n + Tc "c )
and F = exp[ (Tc "c )1 ]. Therefore,
) (Tc "c )
Fc ("c ; "n ! 1) = (1 =
; A = (1
(1
) 1
exp[ (Tc )1 "c
(1
)
1
]
]
and Z
0
1
Fc ("c ; "n ! 1)d"c = =
Z
1
0
(2) When "n = A = (1
Z
1
)(Tc )1 "c
(1
(1
) 1
exp[ (Tc )1 "c
(1
)
1
=1
]d"c
0 (1
d exp[ (Tc )1 "c d"c
)
]
= exp[ (Tc )1 "c
(1
)
])
0
!c ", !n c
) [Tn "c (
!c ) !n
+ Tc "c )
= (1
) ("c ) B
; B = Tn (
!c ) !n
+ Tc
and,
F ("c ; "n =
!c !c "c ) = expf [Tn "c ( ) !n !n 40
+ Tc "c ]1 g = exp[ B 1 ("c )1 ]
Therefore, !c "c ) = (1 !n = (1 ) T c "c
) ("c ) B
Fc ("c ; "n =
(1
) 1
B
exp[ B 1 ("c )1 ][Tc "c
exp[ B 1 "c
(1
)
1
]
]
and Z
1
Fc ("c ; "n
0
Z 1 !c = "c )d"c = (1 ) Tc "c (1 ) 1 B !n 0 Z 1 (1 ) d exp[ B 1 "c ] 1 = Tc B d"c 0 1 1 1 = Tc B exp[ B "c (1 ) ]) 0 = Tc B
exp[ B 1 "c
(1
)
]d"c
1
(3) Using (1) and (2) above we have pn = 1
Tc B
1
=
Tn (! c ) (! n ) Tn (! n ) = Tc + Tn (! c ) (! n ) Tc (! c ) + Tn (! n )
This is equation (8).
8.2
Proposition 2
To simplify notation, we drop the superscript k. We note that the Frechet distribution is max stable; i.e. the max of Frechet variables is still Frechet. To be speci…c, consider the random variable " = maxfwc hc "c ; wn hn "n g. By our discussions in section 3, " = wn hn "n if and only if the individual chooses occupation n. We now obtain the cdf of the distribution of " Pr("
y and wn hn "n
y) = Pr(wc hc "c y y = F( ; ) wc hc wn hn = exp[ B1 y
(1
)
]; B1 =
Tc
wc hc P
y)
+ Tn
wn hn P
1
where we have used the Frechet distribution (1) in the second equality. Consider the mean of non-cognitive workers’ net income, In , conditional on choosing the non-cognitive occupation, n. By the expression of In , (7), we know that it is 41
1
proportional to the mean of (wn hn "n ) 1 , conditional on choosing occupation n. This 1 conditional mean is, by Bayesian rule, the mean of (wn hn "n ) 1 for those choosing oc1 cupation n, divided by the employment share pn . The mean of (wn hn "n ) 1 for those 1 choosing occupation n, in turn, is the mean of (" ) 1 for all workers times the employment share pn . As a result, the conditional mean of In is proportional to the mean of 1 (" ) 1 , which equals Z 1 Z 1 (1 ) 1 d exp[ 1 B y ] 1 )y (1 ) 1 dy y1 = y 1 exp[ B1 y (1 ) ]B1 (1 dy 0 0 We then use change-of-variables to calculate the value of this expression, because the Gamma function is de…ned as Z 1 (a + 1) = ta e t dt; 0
1
where a is a constant. Let x = B1 y (1 ) . Then y = ( Bx1 ) (1 ) , and dy = In addition, as y ! 0, x ! 1; as y ! 1, x ! 0. Therefore, Z 1 1 d exp[ B1 y (1 ) ] 1 y dy Z0 1 1 y 1 exp[ B1 y (1 ) ]B1 (1 )y (1 ) 1 dy = Z0 0 1 1 x x 1+ (1 ) 1 ( ) (1 )(1 ) e x B1 (1 = )( ) (1 ) [ ]B1 (1 ) x B B1 (1 ) Z11 1 1 1 1 x ( ) (1 )(1 ) + (1 ) +1 (1 ) 1 e x dx = B1 0 Z 1 1 1 1 1 (1 ))(1 ) = B1 x (1 )(1 ) e x dx = B1 (1 ))(1 ) (1 (1 )(1 0 1 1 = [Tc (wc hc ) + Tn (wn hn ) ] (1 ) ; = (1 ) (1 )(1 ) Therefore, the average net income of non-cognitive workers, In , equals (1 1 Tn ( wPn hn ) ] (1 ) .This is equation (9).
8.3
1
1 B (1 (1 ) 1
1 (1
)
1
)
)
x
)
dx
)
)
1
[Tc ( wPc hc ) +
Proposition 3 1
We again drop the superscript k. We start with the expression hi e "i = ( wi ) 1 (hi "i ) 1 , which we show in the text, right above Proposition 3. Using this expression and the 42
1 (1
1
dx.
equation of net income, (7), we get Ii
hi e "i = ( wi ) 1
(1
)
1
(wi ) 1
=
1
Ii (1
)wi
This means that Li = Lpi E (hi e "i jOccupation i) = Lpi =
Lpi (1 (1 )wi
)
1
1 (1
)wi
E(Ii jOccupation i)
[Tc (wc hc ) + Tn (wn hn ) ]
1 (1
(33)
)
where the last equality is by Proposition 2. To simplify this expression, we use Proposition 1 to get Ti ( wPi hi ) wc wn Tc ( hc ) + Tn ( hn ) = P P pi This allows us to obtain 1 Lpi wn wc hc + Tn hn ] (1 ) (1 ) 1 [Tc (1 )wi P P wi 1 1 Ti ( P hi ) Lpi 1 wi Ti = [ ] (1 ) = 1 Lpi (hi ) 1 ( ) 1 ( ) wi pi P pi 1 " # 1 1 wi Ti = Lpi hi P pi
Li =
8.4 8.4.1
1 (1
)
Derivations of Various Equations Equation (26)
By Proposition 1 we have Tc (wck hkc ) pkc = pkn Tn (wnk hkn ) Substitute out the ratio wck =wnk using equation (??), and we get equation (26).
43
8.4.2
Equation (25)
Using equations (11) and (8), we can show that wck Lkc
=
Lk pkc
=
Lk
=
Lk
k
1
( (P ) )
Tc
wck hkc
Tc wck hkc
( (P k ) 1 )
Tc (wck hkc ) + Tn (wnk hkn ) 1 1
+
((P k ) 1 ) 1 Tc wck hkc
1=
Tn wnk hkn
1=(1
Tc wck hkc
[Tc wck hkc
)
1=
+ Tn wnk hkn
+ Tn wnk hkn ]
1
1
1=(1
)
1
1
By analogy we have wn Lkn = Lk
1 1
((P k ) 1 ) 1 Tn wnk hkn
[Tc wck hkc
+ Tn wnk hkn ]
1
1 1
1
Adding up these equations we get 1
wc Lkc + wn Lkn =
Lk
1
=
Lk
1
1
((P k ) 1 ) 1 [Tc wck hkc
+ Tn wnk hkn ][Tc wck hkc
((P k ) 1 ) 1 [Tc wck hkc
+ Tn wnk hkn ]
+ Tn wnk hkn ]
1
1 1
Using the output identity P k y k = wck Lkc + wnk Lkn ; we have wck Lkc + wnk Lkn Pk 1 k 1 = (P ) Lk 1 ((P k ) 1 ) 1 [Tc wck hkc
yk =
=
Lk
1 1
1
((P k ) 1 ) 1 [Tc wck hkc
+ Tn wnk hkn ]
+ Tn wnk hkn ]
1
1 1
1
1 1
This expression and equation (??) imply that E k Lk = y k ; i.e. equation (29) still holds under open economy. 8.4.3
Equation (26)
Using equations (??), (??) and (11), we can show that Sk
Lkc Lk pk = b ck ( (P k ) 1 ) wc pk E k = b ck wc (P k ) 1 pk E k () wck = b ck S (P k ) =
b
Tc wck hkc
1
=b
+ Tn wnk hkn
pkc E k 1 Sk (P k )
44
1
1=
1=(1
)
1
1 1
1
+ Tn wnk hkn =
We now use equation (8) to obtain that Tc wck hkc expression allows us to substitute out the term Tc wck hkc giving us, together with equation (??), that Sk = b =
Lkc Lk
bpkc
hkc (
= b(pkc )1
k
1
(P )
1 (1
)
wck ) (Tc )
1
k
We then substitute out wck using b Spck E Sk
= b(pkc )1 = (
1 (1
1 1 11 ) b Sk
, Sk = b
1
)
1
(Tc )
1
(Tc )
(Tc ) (1
1 )
k
1 (1
1 (P k )
1
)
1 (1
)
(pkc )1
yk ) hkc k L
where we have used the relationship E k Lk = equation (30). 8.4.4
1 pkc E k 1 ) 1 (hkc ) 1 k k 1 S (P ) 1 1 Ek 1 +1 (1 ) ( ) (hkc ) 1
((P k ) 1 b
(
1
to obtain
)
1
)
((P k ) 1 wck ) 1 (hkc ) 1
1 (1
(pkc )1
. This
+ Tn wnk hkn in equation (11),
!1=(1
1=
Tc pkc
Ti (wik hki ) pi
y k . The log of this expression is
Equation (32)
The comparative static exercise involves changing hkc and hkn , holding the other parameters …xed, and tracing out the responses of the endogenous variables. First, the identity pkn + pkc = 1 implies that pk d ln pkn = (d ln pkc ) kc pn Next, equations (26), (30) and (31) imply, respectively, that (d ln pkc ) d ln S k
d ln pkn =
( +
d ln y k = (1
1) (d ln hkc 1 1
)d ln pkc + d ln hkc
and d ln y k
d ln S k = 45
d ln hkn )
1
d ln pkc
These four equations are all log linear, and we can solve for d ln y k , d ln S k , d ln pkc , and d ln pkn in terms of d ln hkc and d ln hkn . The solution for d ln S k is equation (32).
9
General Productivity Decomposition
Start with pkc P k y k = wck Lkc so
h 1 yk 1 = Tc wck hkc k k k L P P and so relative to the base country we have " P0 1 y k =Lk wck hkc 0 = p c y 0 =L0 Pk wc0 h0c
+ Tn wnk hkn
i
1 (1
#
+ p0n
wnk hkn wn0 h0n
p0n
wc0 wnk hkn wck wn0 h0n
)
1 (1
)
rearranging y k =Lk = y 0 =L0
wck =P k wck =P k
1 1
"
hkc h0c
p0c
Substituting for the relative wages we have 2 k
k
y =L = y 0 =L0
1
wck =P k wck =P k
1
6 0 6pc 4
hkc h0c
0
k
y =L = y 0 =L0
1
wck =P k wck =P k
1
From the price index we have Pk = =
1 k
wck k
6 0 6pc 4
hkc h0c
pkn +nxkc pkc nxkc
0
p0n +nx0c p0c nx0c
B + p0n @
(Ac ) (wck )1
p0n +nx0c p0c nx0c
B + p0n @
and for the relative real wage of cognitive labor 2 k
+
1
1 1
1 1
1
pkn +nxkc pkc nxkc
+ (An ) (wnk )1 ! 1 1 1 k wc (Ac ) + (An ) wnk 46
1
1
#
13 hkn C 7 A7 h0 5
)
1 (1
)
1 (1
)
n
13 hkn C 7 A7 h0 5 n
1 1
1 (1
and so wck = Pk
k
1
wck wnk
(Ac ) + (An )
!
1 1
and subbing for relative prices, we have wck Pk
k
=
=
k
=
k
0
Ac An
@(Ac ) + (An )
1
pkc
+
nxkc nxkc
1 1
!
1
1
1 1
A
1
pk + nxkc (Ac ) + (Ac ) nk pc nxkc
(Ac )
pkn pkc
1
1
1
nxkc
1
so relative real wage is wck =P k = wc0 =P 0
k
nxkc nx0c
pkc p0c
0
1 1
So substitute this into the decomposition to obtain
k
y k =Lk = y 0 =L0
pkc p0c
0
2
6 6 = 6 4 2
6 6 = 6 4
2
6 = 6 4
k 0
k 0
k 0
pkc p0c 0
B 0 Bpc @ 0
B 0 @pc
nxkc nx0c
nxkc nx0c
pkc p0c
p0c pkc
1 1
1 1
6 0 6pc 4
0
B 0 Bpc @ 1
1 1
hkc h0c
hkc h0c
0
hkc h0c
B + p0n @ 0
hkc h0c
1
nxkc nx0c
nx0c nxkc
2
!11
B + p0n @ !
!
+
+
p0n
p0n
1 1
1
0
1
1
13 hkn C 7 A7 h0 5
1 (1
)
n
3 1 1 11 1 7 hkn C C 7 C 7 A h0 A 5 n
1
nxkc nx0c
0 0 @ pn + nxc pkn + nxkc
Closed Economy Productivity Decomposition,(21) and (22) 47
1
pkn +nxkc pkc nxkc
B pkc @ 0 pc
1
pkn +nxkc pkc nxkc
p0n +nx0c p0c nx0c
0
1
p0n +nx0c p0c nx0c
1
p0n +nx0c p0c nx0c
1 1
1
pkn +nxkc pkc nxkc
1
1
3 1 1 11 1 hkn A C 7 A 7 5 h0n
1
3 1 1 11 1 7 hkn C C 7 C AA 7 0 h 5 n
Starting with the …nal good production function, we have yk =
k
k
=
1
Ac Lkc Lkc
1
+ An Lkn 1
Lkn Lkc
Ac + An
!
1
1
The …rst-order condition for optimal input choice requires Lkc = Lkn
pkc An pkn Ac
1
:
Substituting this expression into the output equation yields yk =
k
Lkc
Ac pkc
1
Educational and occupational choice requires that wck Lkc = pkc y k . Substituting this expression into the output equation, we obtain wck =
k
1
pkc
1
(Ac )
(34)
1
Rearranging the educational expenditure equation, Eck
wck hkc
=
1 1
1 (1
Tc pkc
)
;
and substituting E k = y k =Lk , we can substitute wck in equation (34) to obtain after rearranging 1 1 1 yk k k k ( 1) = hc pc ; (Ac ) 1 (Tc ) Lk where we have de…ned 0
yk =@ Lk
k k hc
1. Substituting out pkc using its de…nition, we obtain
+
1+
Tn hkn Tc (hkc )
wnk wck
!
(
1)
(Ac )
Finally, factor market clearing implies wck wnk
=
"
Tn Tc
Ac An 48
hkn hkc
#1
:
1
(Tc )
1
111 A
:
Substituting this expression into the GDP per capita equation and simplifying, we obtain an expression with no endogenous variables 0
yk B =@ k L
k k hc
0
Tn hkn
@1 +
Tc (hkc )
!
1
1
An Ac
(
1)
A
(Ac )
1
(Tc )
1
111 C A
:
Comparing GDP per capita in country k to a base country (or to the initial values for that country in a comparative static, we have 1 0 ! ( 1) 1 1 1 C B hk 1 + Tn (hkn ) An C B k c Ac k k k T h c( c ) C B y =L C B : = C 0 1 y 0 =L0 B ( 1) C B (h0n ) An A @ h0c 1 + TTn(h 0) Ac c
c
Combining the occupational share equations and labor market clearing conditions for the base country, we have An Ac
1
Tn Tc
(h0c )
=
(h0n )
!
1
p0n : p0c
Substituting this expression into the relative GDP per capita expressions and simplifying, we arrive at our decomposition: 0 111 0 1 y k =Lk B =@ y 0 =L0
9.1
k
0
@p0c
hkc h0c
(
1)
+ p0n
hkn h0n
(
1)
(
A
1)
C A
:
Free Trade Productivity Decomposition
Under free trade, a single wc and wn prevails everywhere. The value of output must be equal to the value of income and so P k y k = wc Lkc + wn Lkn ; P k = (
k
)
1
The supply of type i labor in country k is given by Lki
Lk pki = wi
(
k
)
Tc
wc hkc 49
+
Tn wn hkn
1=
1=(1
)
So we can write real output per capita in country k relative to a base country 0 as k
k
0
0
y =L P @ = y 0 =L0 Pk
Since P k =
k
1
wc hkc
Tc
0
Tc (wc h0c ) + Tn (wn h0n )
+
0
k
y =L =@ y 0 =L0
wc hkc
wn hkn
k
Tc
0
Tc (wc h0c ) + Tn (wn h0n )
+ Tn
Rearranging, we obtain k
0
y =L =@ y 0 =L0
k 0
A
, we have k
k
!1 111
Tn wn hkn
k
Tc (wc h0c ) Tc (wc h0c ) + Tn (wn h0n )
Tc
wc hkc
Tc (wc h0c )
!
+
!1 111 A
Tn (wn h0n ) Tc (wc h0c ) + Tn (wn h0n )
Tn wn hkn Tn (wn h0n )
now replacing the expressions with occupation shares from the base country, we obtain k
k
0
y =L =@ y 0 =L0
k 0
p0c
hkc h0c
+ p0n
hkn h0n
!1 111 A
So, the di¤erence with the closed economy is in the exponents. Note, however, that since this is holding …xed relative prices it cannot be thought used to talk about comparative statics as was the case in the closed economy.
10
Data Appendix
1. Sample Cuts for NLSY-79 Data Following Neal and Johnson (1996) we: (1) use the 1989 version of AFQT and drop the observations with missing AFQT scores; (2) drop those whose wage exceeds $75 or below $1 in 1991; and (3) drop those who are older than 17 when they take the AFQT. 2. O*NET Data The following is the list of O*NET task ID’s of the measures we discuss in the text. Leadership is 4.A.4.b.4, and enterprising 1.B.1.e. Enterprising skills involve “starting up and carrying out projects”and “leading people and making many decisions”. 50
!! 1 1
A
In addition, we have experimented with the following candidate measures. (1) Originality is about coming up with “unusual or clever ideas about a given topic or situation”, or developing “creative ways to solve a problem”. 1.A.1.b.2. (2) Social skills involve “working with, communicating with, and teaching people”. 1.B.1.d. (3) Artistic talents show up when “working with forms, designs and patterns”, where “the work can be done without following a clear set of rules”. 1.B.1.c 2. (4) Investigative skills involve “working with ideas”and “searching for facts and …guring out problems mentally”, and require “an extensive amount of thinking”; 1.B.1.b. The results are in Table A1. When we use originality, social skills or investigative skills to measure noncognitive skills, the AFQT coe¢ cient of the non-cognitive sub-sample is larger than the cognitive sub-sample. This is counter-intuitive. On the other hand, for the artistictalent sub-sample, the AFQT coe¢ cient is negative, meaning that the artists with higher test scores have lower wages. However, out of the NLSY-79 sample of over 3000, there are only 30 artists, less than 1% of the sample size. 3. ILO Employment-by-Occupation Data We map the O*NET occupation codes into the ISCO-88 codes using the crosswalk at the National Crosswalk center ftp://ftp.xwalkcenter.org/DOWNLOAD/xwalks/. We drop the following observations from the ILO raw data because of data quality issues. 1. All data from Cyprus, because the data source is o¢ cial estimate (source code “E”). 2. Year 2000 for Switzerland, because over 1 million individuals, a large fraction of the Switzerland labor force, are “not classi…ed”. 3. Uganda, Gabon, Egypt, Mongolia, Thailand, Poland in 1994 and Romania in 1992, because the aggregate employment of the sub-occupation categories does not equal the number under “Total”. 4. Estonia in 1998, S. Korea in 1995, and Romania in 2000, because the data is in 1-digit or 2-digit occupation codes. Most countries have a single year of data around 2000. In Figure A1 we plot the non-cognitive employment share for all the countries that have multiple years of data. Within countries the non-cognitive employment share shows very limited variation over time. As a result, for this set of countries we keep the single year of data closest to 2000; e.g. 1990 for Switzerland, 2000 for U.S. and Australia, etc. By construction, the non-cognitive and cognitive employment shares sum to 1 by country. 4. Test Score Data We have tabulated over-time changes of PISA scores within countries and found very little variation. For example, for the U.S. reading score the mean is 499.26 and the 51
standard deviation is 3.93. We list these summary statistics by country by subject in Table A2. There have been several international tests on adults: IALS (International Adult Literacy Survey), administered in 1994-1998, ALLS (Adult Literacy and Life Skills Survey), conducted in 2002-2006, and PIAAC (Program for the International Assessment of Adult Competencies), conducted in 2013. The response rate of IALS, 63%, is substantially lower than the initial wave of PISA in 2000, 89% (Brown et al. 2007). ALLS was designed as a follow-up to IALS, but only 5 countries participated. Of the 28 countries in our sample, only 18 participated in IALS, and only 21 in PIAAC. This would represent a 36% and 25% reduction in the number of observations, respectively. We regress the 2012 PISA scores on 2013 PIAAC scores, for reading and math, for all the countries that participated in both tests, including those that are not in our sample. We obtain, respectively, the coe¢ cient estimate of 0.938 and 1.067, and R-square of 0.508 and 0.527. 5. Correlation Coe¢ cients of Output TFP Estimates In Table A4 we report the full correlation table among our output TFP estimates, k , and those reported in the literature. Ours = our estimates for k ; HJ98 = Hall and Jones (1998) TFP (A); KRC97 = Klenow and Rodriguez-Clare (1997); EK96 = Eaton and Kortum (1996); HR97 = Harrigan (1997); PWT_90 = Penn World Tables 8.0, current PPP, year 1990; PWT_00 = PWT 8.0, current PPP, 2000; EK 02 = Eaton and Kortum (2002). The correlation coe¢ cients between our k and the literature’s estimates, reported in the …rst column of Table A4 and in boldface, are comparable to those among the literature’s estimates, reported in the rest of Table A4.
52
Figure 1 Test Score and Educational Spending Per Capita
4.8
4.85
4.9
4.95
5
5.05
Figure 2 Normalized Test Scores and Cognitive Employment Shares
-.35
-.3
-.25 -.2 log(Cognitive Emp. Share)
log PISA math, adj. by output/worker
-.15
-.1
Linear prediction
30
Figure 3 Cognitive-Productivity Ranking vs. PISA-Math Ranking
Luxembourg Italy United States France Greece Norway Australia
20
Spain Germany
Ranking, hkc
Portugal New Zealand Sweden Denmark Ireland Switzerland Slovenia Korea, Republic of
10
Austria Hong Kong, China United Kingdom Hungary Iceland Poland Slovakia Czech Republic
0
Belgium Netherlands Finland
0
10
20
30
Ranking, PISA math
30
Figure 4 Non-Cognitive-Productivity Ranking vs. PISA-Math Ranking
Korea, Republic of Switzerland Hong Kong, China Germany Slovenia France
20
Italy Portugal
Ranking, hkn
Australia Denmark Poland Sweden Luxembourg Norway Hungary Spain Czech Republic
10
United States Slovakia Iceland Ireland Greece Austria New Zealand United Kingdom
0
Belgium Finland Netherlands
0
10
20
30
Ranking, PISA math
1.3
Figure 5 Overall Education Quality
Finland
Cognitive Productivity 1 1.1 1.2
Netherlands Belgium Czech Republic Slovakia Poland Iceland Hungary United Kingdom Hong Kong, China Austria Korea, Republic of Slovenia Switzerland Ireland Denmark Sweden New Zealand Portugal Germany Australia Spain Norway Greece France United States
Italy
.9
Luxembourg
0
.5
1 1.5 non-cognitive productivity
2
2.5
Iso-Edu-Quality
1.4
Figure 6 Overall Education Quality: Extended Sample
Cognitive Productivity 1 1.1 1.2 1.3
ESTONIA
Finland
LATVIA Czech Republic Slovakia Poland Iceland Korea, Hong Republic of Kong, China Hungary Slovenia Austria Switzerland Ireland Denmark BULGARIA Portugal Sweden Germany Spain ROMANIA Norway France Australia Greece Italy
Netherlands Belgium United Kingdom New Zealand
United States Luxembourg
.9
THAILAND
LITHUANIA
0
1 2 non-cognitive productivity cognitive productivity
3
Iso-Edu-Quality
1.3
Figure 7 Overall Education Quality: Free-trade Counterfactual
Finland
Cognitive Productivity 1 1.1 1.2
Netherlands Czech Republic Slovakia Poland Iceland Hungary Hong Kong, China Austria Korea, Republic of SwitzerlandSlovenia Ireland Denmark Sweden Portugal Germany Australia Spain Norway France Italy
Belgium
United Kingdom
New Zealand Greece
United States
.9
Luxembourg
0
.5 cognitive productivity
1 1.5 non-cognitive productivity
2
2.5
Iso-Edu-Quality, free trade counterfactual
Table 1 Test Score and Wages of Non-cognitive and Cognitive Occupations (1) VARIABLES Black Hispanics Age
Replicate -0.0537*** (0.0196) 0.0425** (0.0211) 0.0349*** (0.00708)
(2) Non-Cog. SubSample -0.0937** (0.0365) 0.0164 (0.0378) 0.0483*** (0.0129)
(3) Cog. SubSample -0.0381* (0.0228) 0.0482* (0.0251) 0.0285*** (0.00833)
0.183*** (0.0113) -0.00717 (0.00961)
Interaction -0.0661*** (0.0191) 0.0413** (0.0206) 0.0323*** (0.00689) 0.121*** (0.0163) 0.187*** (0.0264) 0.137*** (0.0115) -0.0369*** (0.00950)
(5) Alt. Leadership -0.0641*** (0.0192) 0.0414** (0.0206) 0.0316*** (0.00690) 0.127*** (0.0186) 0.195*** (0.0263) 0.125*** (0.0113) -0.0358*** (0.00956)
0.183*** (0.00964) -0.0130 (0.00802)
0.157*** (0.0182) -0.0199 (0.0143)
6.281*** (0.132) 2,259 0.163
-0.0345** (0.0159) 0.0525** (0.0245) 6.218*** (0.109) 3,210 0.214
-0.00749 (0.0182) 0.0495** (0.0244) 6.232*** (0.109) 3,210 0.211
Non-cog. Occp. College AFQT AFQT2 AFQT x NonCog. AFQT x College Constant Obs. No. R2
6.233*** (0.112) 3,210 0.168
6.148*** (0.205) 951 0.151
(4)
Notes: The dependent variable is log wage, and the sample is NLSY 79. Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
Table 2 Summary Statistics Variable Labor Force Size Non-cog. Emp. Share Cognitive Emp. Share Agg. Output ($000) Edu. Exp./Output PISA Reading Score PISA Math Score PISA Science Score | | | |
Obs 28 28 28 28 20 28 28 28 27 27
Mean 12541.24 0.2425 0.7575 4.59E+08 0.1255 498.96 503.73 506.81 0.0414 0.0454
Std. Dev. 23132.62 0.0514 0.0514 1.18E+09 0.0194 18.30 22.17 19.70 0.0471 0.0776
Min 156.43 0.1157 0.6225 4130208 0.0985 468.93 455.80 470.07 0.0002 0.0002
Max 120464.70 0.3775 0.8843 6.25E+09 0.1695 539.34 553.40 554.28 0.1693 0.3856
Table 3 Sample Countries, Years and Rankings
Country Australia Austria Belgium Czech Republic Denmark Finland France Germany Greece Hong Kong Hungary Iceland Ireland Italy S. Korea Luxembourg Netherlands New Zealand Norway Poland Portugal Slovakia Slovenia Spain Sweden Switzerland United Kingdom United States
Year 2000 2000 2000 2000 2000 2000 2000 2000 2000 2001 2000 2000 2000 2000 2000 2000 2000 1996 2000 2000 2000 2000 2000 2000 2000 1990 2000 2000
Cog-Prod Rank 22 11 3 4 16 1 25 20 24 10 8 7 15 27 12 28 2 18 23 6 19 5 13 21 17 14 9 26
PISA Math Rank 8 11 6 13 10 3 15 9 28 1 23 12 17 27 2 22 5 7 20 16 26 21 14 24 18 4 19 25
Non-Cog Prod Rank 20 6 3 12 19 2 23 25 7 26 14 9 8 22 28 16 1 5 15 18 21 10 24 13 17 27 4 11
Table 4 Patterns of Trade
Non-cog abundance x non-cog intensity Cap abundance x cap intensity Skill abundance x skill intensity constant
Dep. Var. = net exp./(imp.+exp.) (1) (2) (3) 15.989 15.979 10.615 (2.92) (2.92) (2.02) 0.000 0.000 (0.10) (0.22) 9.173 (4.71) -1.108 -1.113 1.976 (-3.30) (-3.28) (2.77)
industry FE country FE
yes yes
yes yes
yes yes
R2 # obs.
0.369 1103
0.369 1103
0.401 1103
Table 5 Value of θ Dependent Variable = normalized test score, equation (30) VARIABLES ASNZ Constant Observations R2
(1) (2) (3) (4) (5) 0.717*** 0.714*** 0.696*** 0.521*** 0.512** (0.230) (0.224) (0.223) (0.165) (0.201) 0.213** 0.208*** 0.189*** 0.189** (0.0773) (0.0574) (0.0570) (0.0695) 5.076*** 5.075*** 5.072*** 5.032*** 5.040*** (0.0624) (0.0607) (0.0608) (0.0448) (0.0546) 26 28 28 28 28 0.288 0.347 0.393 0.384 0.292
(6) 0.677* (0.357) 0.175** (0.0842) 5.032*** (0.0784) 28 0.196
(7) 0.565** (0.198) 0.210** (0.0682) 5.020** (0.0547) 34 0.302
Notes: ASNZ is the dummy for Australia and New Zealand, whose raw occupation-employment data are in different classification codes as compared with the other countries in our sample.
VARIABLES ln 1
ASNZ Constant
Obs. No. R2
(1)
(2)
2.979** (1.174) -1.074** (0.415) 3.497*** (0.319)
2.964** (1.207)
27 0.291
Table 6 Value of α (3) (4) (5)
(6)
(7)
(8)
3.501*** (0.328)
2.889** (1.151) -1.075*** (0.304) 3.522*** (0.314)
2.781** (1.123) -1.049** (0.397) 3.541*** (0.305)
2.779** (1.163) -1.051** (0.411) 3.532*** (0.316)
3.562* (1.864) -0.973** (0.440) 3.520*** (0.409)
3.125** (1.224) -1.094** (0.423) 3.465*** (0.332)
3.872** (1.100) -1.246*** (0.379) 3.004*** (0.274)
25 0.208
27 0.366
27 0.291
27 0.277
27 0.209
28 0.282
34 0.363
Notes: ASNZ is the dummy for Australia and New Zealand, whose raw occupation-employment data are in different classification codes as compared with the other countries in our sample.
Table 7 Summary of Parameter Values and Identification Parameters
Intuition
Values
Identification
0.1255
Edu. spending as share of output, (20)
2.0877~3.4965
Strength of selection effect, (21)
1.4706~1.5200
α
Elasticity in Human Cap Prod Dispersion of Innate Ability Sub Elasticity in Agg Production
Θk
Output TFP
Table 8
Agg. production function, (22) Output per worker, test score and relative emp. share, given α, (22)
TFP of Cognitive Education
Table 3
Normalized test score and cog. emp. share, given θ and η, (21)
TFP of Non-cognitive Education
Table 3
Revealed comp advantage by relative emp. share, given α and θ, (19)
η θ
Table 8 Contributions of Overall Education Quality to Output per Worker Trade Cost Closed Econonomy (1) (2) (3) (4) (5) Contribution Contribution of Contribution Contribution of Output Per of Output Overall Edu of Output Overall Edu Countries Worker TFP Quality TFP Quality Austria 0.6434 0.5645 1.1399 0.5297 1.2147 Belgium 0.6892 0.5301 1.3001 0.4636 1.4867 Czech Republic 0.3293 0.2982 1.1045 0.2860 1.1513 Denmark 0.5979 0.7037 0.8496 0.6187 0.9664 Finland 0.5037 0.3326 1.5145 0.3259 1.5458 France 0.7329 0.8720 0.8405 0.8517 0.8606 Germany 0.6296 0.7088 0.8883 0.7126 0.8834 Greece 0.5190 0.5144 1.0089 0.4761 1.0901 Hong Kong 0.6864 0.7840 0.8755 0.7724 0.8887 Hungary 0.3517 0.3375 1.0419 0.3292 1.0684 Iceland 0.5110 0.5139 0.9943 0.4168 1.2261 Ireland 0.6642 0.5136 1.2930 0.5583 1.1896 Italy 0.6761 0.7982 0.8470 0.7977 0.8476 S. Korea 0.4304 0.6267 0.6868 0.6027 0.7142 Luxembourg 1.4376 1.5674 0.9172 1.5674 0.9172 Netherlands 0.6712 0.4624 1.4515 0.4387 1.5300 Norway 0.7289 0.8704 0.8374 0.7589 0.9605 Poland 0.3045 0.2979 1.0219 0.2917 1.0438 Portugal 0.3845 0.4195 0.9165 0.4216 0.9121 Slovakia 0.2979 0.2732 1.0901 0.2600 1.1459 Slovenia 0.3929 0.4406 0.8918 0.4275 0.9191 Spain 0.6087 0.5979 1.0180 0.5913 1.0293 Sweden 0.5937 0.6389 0.9292 0.5917 1.0034
(1)
Countries Switzerland United Kingdom United States
Output Per Worker 0.5855 0.6349 1.0000
Table 8 Continued Trade Cost (2) (3) Contribution Contribution of of Output Overall Edu TFP Quality 0.9880 0.5926 0.5040 1.2597 1.0000 1.0000
Closed Econonomy (4) (5) Contribution Contribution of of Output Overall Edu TFP Quality 0.6641 0.8816 0.4758 1.3345 1.0000 1.0000
Notes: Columns (4) and (5) are obtained using equations (15) and (16), and columns (6) and (7) obtained using equation (28). Table 9 Robustness Exercises Cog Productivity Value Ranking closed-economy, θ = 2.0887, 0.9844 0.9583 closed-economy, θ = 2.0887, α = 2 0.9844 0.9583 Free-trade, θ = 3.4965 Identical Identical Free-trade, θ = 2.0877 Identical Identical
Non-cog Productivity Value Ranking
Overall Edu Quality Value Ranking
1.0000
0.9998
0.9888
0.9788
0.9906
0.9972
0.9798
0.9740
0.9160
0.8577
0.8365
0.7757
0.9562
0.9316
0.8824
0.8058
Notes: This table reports the correlation coefficients between the values and country rankings of cognitive productivity, non-cognitive productivity, and overall educational quality under our main specification and under alternative parameter values and settings.
Table 10 Output/Worker Relative to the U.S.: Data and Counterfactual Values
Countries Austria Belgium Czech Republic Denmark Finland France Germany Greece Hong Kong Hungary Iceland Ireland Italy S. Korea Luxembourg Netherlands Norway Poland Portugal Slovakia Slovenia Spain Sweden Switzerland United Kingdom United States
Data 0.6434 0.6892 0.3293 0.5979 0.5037 0.7329 0.6296 0.5190 0.6864 0.3517 0.5110 0.6642 0.6761 0.4304 1.4376 0.6712 0.7289 0.3045 0.3845 0.2979 0.3929 0.6087 0.5937 0.5855 0.6349 1.0000
Free-trade Counterfactual 0.6910 0.8367 0.3480 0.7222 0.5421 0.8276 0.6969 0.5888 0.8210 0.3683 0.5885 0.5847 0.7306 0.6484 1.4475 0.8541 0.8726 0.3293 0.4169 0.3173 0.4558 0.6170 0.6562 1.0084 0.7131 1.0000
%, Data to Free Trade 7.39% 21.40% 5.66% 20.79% 7.61% 12.91% 10.70% 13.46% 19.61% 4.73% 15.18% -11.96% 8.06% 50.63% 0.69% 27.24% 19.71% 8.16% 8.42% 6.53% 16.01% 1.36% 10.54% 72.24% 12.31% 0.00%
Figure A1 Non-Cognitive Employment Share Over Time for Select Countries
Poland
Portugal
.25 .2
1970 1980 1990 2000 2010
United States
.3
.35
Switzerland
.2
.25
Non-Cog. Emp. Share
.3
.35
Australia
1970 1980 1990 2000 20101970 1980 1990 2000 2010
YEAR Graphs by COUNTRY
Table A1 Neal-Johnson Regressions for Alternative Measures of Non-Cognitive Skills
VARIABLES Black Hispanics Age AFQT AFQT2 Constant Obs. No. R2
Originality -0.0735* (0.0395) 0.0380 (0.0402) 0.0569*** (0.0136) 0.182*** (0.0210) 0.00428 (0.0149) 5.942*** (0.216) 1,096 0.164
Not Originality -0.0463** (0.0216) 0.0398* (0.0240) 0.0220*** (0.00798) 0.154*** (0.0109) -0.0382*** (0.00996) 6.414*** (0.126) 2,114 0.126
Social-skill 0.0238 (0.0683) 0.119 (0.0788) 0.0557** (0.0254) 0.204*** (0.0370) -0.00483 (0.0341) 5.732*** (0.403) 382 0.127
Not Socialskill -0.0515** (0.0202) 0.0364* (0.0215) 0.0325*** (0.00722) 0.185*** (0.00979) -0.0172** (0.00807) 6.292*** (0.114) 2,828 0.181
Artistic -1.490* (0.799) -0.586* (0.331) 0.0752 (0.0844) -0.713** (0.333) 0.299* (0.150) 6.061*** (1.357) 30 0.188
Not Artistic -0.0533*** (0.0195) 0.0422** (0.0212) 0.0345*** (0.00710) 0.184*** (0.00965) -0.0120 (0.00809) 6.239*** (0.112) 3,180 0.170
Investigative 0.010 (0.091) 0.036 (0.092) 0.027 (0.030) 0.188*** (0.060) -0.043 (0.032) 6.642*** (0.481) 158 0.106
Not Investigative -0.060*** (0.02) 0.039* (0.022) 0.036*** (0.007) 0.171*** (0.010) -0.019** (0.008) 6.212*** (0.114) 3052 0.148
Table A2 Within-Country, Over-Time Variations of PISA Scores Country Australia Austria Belgium Canada Czech Republic Denmark Estonia Finland France Germany Greece Hungary Iceland Ireland Italy Japan S. Korea Luxembourg Netherlands New Zealand Norway Poland Portugal Slovak Republic Slovenia Spain Sweden Switzerland United Kingdom United States
Math 515.67 505.54 519.86 526.10 504.52 507.66 515.74 537.98 499.53 508.27 455.80 487.04 505.03 498.24 473.90 530.66 547.42 490.53 529.32 516.13 493.09 499.49 476.53 492.15 502.35 483.22 495.98 530.28 493.93 481.50
Mean Reading 518.66 490.64 505.92 527.32 486.78 494.94 506.00 539.34 497.95 495.06 473.15 485.37 493.19 515.65 481.49 515.24 537.98 479.69 509.88 520.89 499.30 500.41 479.42 468.93 486.27 480.58 503.74 500.46 496.19 499.26
Science 525.21 508.31 507.27 529.54 507.22 497.90 533.54 554.28 497.47 520.06 470.07 500.29 488.18 512.77 485.92 539.19 532.64 487.16 523.05 526.01 493.64 510.57 485.51 483.30 514.91 491.04 494.41 514.46 514.20 496.11
Math 8.69 0.07 6.80 5.96 10.63 7.08 4.34 13.21 7.55 5.66 9.02 6.68 9.20 7.43 11.95 5.92 4.78 1.83 6.49 11.06 4.18 12.23 12.06 7.47 1.83 2.27 13.27 3.07 1.52 5.41
Std. Dev. Reading 7.63 1.05 2.96 4.37 6.20 1.75 8.91 9.63 7.35 8.67 8.53 5.86 10.38 12.05 9.04 17.19 11.42 6.39 2.85 5.89 8.63 14.46 8.77 6.25 7.10 12.12 13.58 5.34 2.74 3.93
Science 3.23 3.58 2.81 4.57 6.25 1.79 7.04 8.94 1.99 4.25 3.33 5.23 9.01 8.00 9.41 7.68 9.09 3.72 1.57 9.02 6.72 14.17 9.87 10.52 3.59 4.69 9.28 2.63 0.53 6.64
Table A3 Correlation between 2012 PISA and 2013 PIAAC scores
PIAAC Literacy
PISA Reading 0.938 (5.18)
PIAAC Numeracy
PISA Math
Constant
249.047 (5.13)
1.067 (5.38) 215.948 (4.13)
Obs. No. R2
28 0.508
28 0.527
Table A4 Correlation Coefficients for Output TFP Estimates
Ours HJ98 KRC97 EK 96 HR97 PWT_90 PWT_00 EK 02
Ours 1.0000 0.5576 0.0031 0.4037 0.0696 0.5965 0.0147 0.4437 0.2708 0.6327 0.0003 0.6276 0.0004 0.5558 0.0205
HJ98
KRC97 EK 96
HR97
PWT_90
PWT_00
1.0000 0.8412 0.0000 0.5348 0.0328 0.5841 0.1284 0.8792 0.0000 0.6878 0.0001 0.4159 0.0968
1.0000 0.7109 0.0020 0.5394 0.1677 0.7401 0.0001 0.2565 0.2617 0.4828 0.0496
1.0000 0.0680 0.8729 0.6976 0.0027 0.3856 0.1402 0.7655 0.0009
1.0000 0.6126 0.1064 -0.5382 0.1688 0.3538 0.3899
1.0000 0.7089 0.0000 0.6114 0.0091
1.0000 0.4646 0.0602
Notes: Ours = our estimates for Θk; HJ98 = Hall and Jones (1998) TFP (A); KRC97 = Klenow and Rodriguez-Clare (1997); EK96 = Eaton and Kortum (1996); HR97 = Harrigan (1997); PWT_90 = Penn World Tables 8.0, current PPP, year 1990; PWT_00 = PWT 8.0, current PPP, 2000; EK 02 = Eaton and Kortum (2002).
